Herbert Amann 

Research papers 


  1. Maximal Regularity for Parabolic Transmission Problems.
    J. Evol. Equ.21, 3375-3420 (2021)   pdf,
  2. Population Dynamics in Hostile Neighborhoods.
    Rend. Istit. Mat. Univ. Trieste. 52, (2020), 27-43.   pdf,
  3. Linear Parabolic Equations with Strong Boundary Degeneration.
    Journal of Elliptic and Parabolic Equations 6, (2020), 123-144   html   pdf,
  4. Cauchy Problems for Parabolic Equations in Sobolev-Slobodeckii and Hölder Spaces on Uniformly Regular Riemannian Manifolds.
    J. Evol. Equ. 17, (2017), 51 - 100.   pdf,
  5. Uniformly regular and singular Riemannian manifolds.
    In: Elliptic and Parabolic Equations, Hannover, September 2013,
    Editors: Escher, J., Schrohe, E., Seiler, J., Walker, C,
    Springer Proceedings in Mathematics & Statistics, (2015), 1- 43 .   pdf
  6. Parabolic equations on uniformly regular Riemannian manifolds and degenerate initial boundary value problems.
    To appear in :"Recent Developments of Mathematical F luid Mechanics",
    Amann, H., Giga, Y., Kozono, H., Okamoto, H., Yamazaki, M. (Eds.)
    Series: Advances in Mathematical Fluid Mechanics, Birkhaeuser-Verlag, 2016.   pdf,
  7. Anisotropic Function Spaces on Singular Manifolds.
    arXiv.1204.0606   pdf,
  8. Function Spaces on Singular Manifolds.
    Math. Nachr. 286, No. 5 - 6, 436 - 475 (2013)   pdf
  9. Anisotropic function spaces and maximal regularity for parabolic problems. Part 1: Function spaces.
    Jindrich Necas Center for Mathematical Modeling Lecture Notes, Prague, Volume 6 (2009).    pdf    prague
  10. Time-delayed Perona-Malik type problems.
    Acta. Math. Univ. Comenianae. LXXVI, (2007), 15 - 38.    ps    pdf
  11. Quasilinear parabolic functional evolution equations.
    In: M. Chipot, H. Ninomiya (editors), Recent Avdances in Elliptic and Parabolic Issues.
    Proc. of the 2004 Swiss - Japanese Seminar, World Scientific, (2006), 19 - 44.    ps    pdf
  12. Quasilinear parabolic problems via maximal regularity.
    Advances in Differential Equations, 10, (2005), 1081 - 1110.    ps    pdf
  13. (with P. Quittner) Optimal control problems governed by semilinear parabolic equations with low regularity data.
    Advances in Differential Equations, 11, (2006), 1 - 33.   ps    pdf
  14. (with P. Quittner) Optimal control problems with final observation governed by explosive parabolic equations.
    SIAM J. on Control and Optimization., 44, (2005), 1215 - 1238.   ps    pdf
  15. (wit Ch. Walker) Local and global strong solutions to continuous coagulation-fragmentation equations with diffusion.
    J. Diff. Equ., 218, (2005), 159-186.  ps    pdf
  16. Maximal regularity for nonautonomous evolution equations.
    Advanced Nonlinear Studies, 4, (2004), 417 - 430.  ps    pdf
  17. Nonautonomous parabolic equations involving measures.
    Zapiski Nauchn. Seminar. POMI, 306, (2003), 16-52.  ps    pdf
    also see: Journal of Mathematical Sciences, 130, (2005), 4780 - 8002.
  18. (with J. I. Diaz) A note on the dynamics of an oscillator in the presence of strong friction.
    Nonlinear Analysis, TM&A. 55, (2003), 209 - 216.   ps   pdf
  19. Maximum principles and principal eigenvalues.
    In: Ten Mathematical Essays on Approximation in Analysis and Topology,
    J. Ferrera, J. López-Gómez, F. R. Ruíz del Portal (editors),
    Elsevier, 2005, 1 - 60.   ps   pdf
  20. Navier-Stokes equations with nonhomogeneous Dirichlet data.
    J. Nonlinear Math. Physics. 10, Supplement 1 (2003), 1-11, Öresund Symposium.  ps   pdf
  21. (with P. Quittner) Semilinear parabolic equations involving measures and low regularity data.
    Transactions AMS. 356, (2004), 1045--1119.   ps    pdf
  22. Linear parabolic equations with singular potentials.
    J. Evolution Equ. (JEE), 3, (2003), 395 - 406.   ps   pdf
  23. Nonhomogeneous Navier-Stokes equations with integrable low-regularity data.
    Nonlinear problems in mathematical physics and related topics, II.
    Int. Math. Ser., Kluwer/Plenum, New York, (2002), 1-28.  ps   pdf
  24. Nonhomogeneous Navier-Stokes equations in spaces of low regularity.
    Topics in Mathematical Fluid Mechanics.
    Quaderni di Matematica 10,(2002), 13-31.  ps    pdf
  25. Linear parabolic problems involving measures.
    Rev. R. Acad. Cien. Serie A. Mat. (RACSAM), 95, (2001), 85-119.   ps   pdf
  26. Elliptic operators with infinite-dimensional state spaces.
    J. Evolution Equ. (JEE), 1, (2001), 143-188.   ps    pdf
  27. (with F. Weber) On a quasilinear coagulation-fragmentation model with diffusion.
    Adv. Math. Sci. Appl., 11, (2001), 227-263.   ps   pdf
  28. Compact embeddings of vector-valued Sobolev and Besov spaces.
    Glasnik Matematicki, 35 (55), (2000), 161-177.  ps    pdf
  29. On the strong solvability of the Navier-Stokes equations.
    J. Math. Fluid Mech., 2, (2000), 16-98.   ps   pdf
  30. Coagulation-fragmentation processes.
    Arch. Rat. Mech. Anal., 151, (2000), 339-366.  ps   pdf
  31. (with P. Quittner) Elliptic boundary value problems involving measures: existence, regularity, and multiplicity.
    Advances in Diff. Equ., 3, (1998), 753-813.   ps    pdf
  32. (with J. López-Gómez) A priori bounds and multiple solutions for superlinear indefinite elliptic problems.
    J. Diff. Equ., 146, (1998), 336-374.   ps   pdf
  33. (with M. Fila) A Fujita-type theorem for the Laplace equation with a dynamical boundary condition.
    Acta Math. Univ. Comenianae, 66, (1997), 321-328.   ps   pdf
  34. Operator-valued Fourier multipliers, vector-valued Besov spaces, and applications.
    Math. Nachr., 186, (1997), 5-56.   ps   pdf
  35. Stability and bifurcation in viscous incompressible fluids.
    Zapiski Nauchn. Seminar. POMI, 233, (1996), 9-29.   ps   pdf
  36. (with P. Quittner) A nodal theorem for coupled systems of Schrödinger equations and the number of bound states.
    J. Math. Phys., 36, (1995), 4553-4560.
  37. Heat-conducting incompressible viscous fluids.
    In: Navier-Stokes Equations and Related Non-Linear Problems,
    A. Sequeira (editor),  231-243. Plenum Press,  New York, 1995.
  38. (with J. Escher) Strongly continuous dual semigroups.
    Ann. Mat. Pura Appl., CLXXI, (1996), 41-62.
  39. Stability of the rest state of a viscous incompressible fluid.
    Arch. Rat. Mech. Anal., 126, (1994), 231-242.
  40. (with M. Hieber and G. Simonett) Bounded H_infinity-calculus for elliptic operators.
    Diff. Int. Equ., 7, (1994), 613-653.  ps   pdf
  41. Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems.
    In: Function Spaces,Differential Operators and Nonlinear Analysis.
    H.J. Schmeisser, H. Triebel (editors),
    Teubner, Stuttgart, Leipzig, 1993, 9-126.  ps   pdf
  42. (with M. Renardy) Reaction-diffusionproblems inelectrolysis.
    Nonlin. Diff. Equ. and Appl., 1, (1994), 91-117.
  43. Multiplication in Sobolev and Besov Spaces.
    In: Nonlinear Analysis, A Tribute in Honour of G. Prodi.
    Quaderni, Scuola Norm. Sup. Pisa, 27-50, 1991.
  44. Highly degenerate quasilinear parabolic systems.
    Ann. Scuola Norm. Sup. Pisa, Ser. IV, 18, (1991), 135-166.
  45. Global existence for a class of highly degenerate parabolic systems.
    Japan J. Indust. Appl. Math., 8, (1991), 143-151.
  46. Hopf bifurcation in quasilinear reaction-diffusion systems.
    In: Delay Differential Equations and Dynamical Systems,
    Proceedings, Claremont 1990,  S. Busenberg,  M. Martelli (editors)
    Lecture Notes in Math. #1475,  53-63, New York, 1991. Springer Verlag.
  47. Dynamic theory of quasilinear parabolic systems - III. Global existence.
    Math. Z., 202, (1989), 219-250; Erratum. 205 (1990),331.
  48. Dynamic theory of quasilinear parabolic equations - II. Reaction-diffusion systems.
    Diff. Int. Equ., 3, (1990), 13-75.   pdf
  49. Dynamic theory of quasilinear parabolic equations - I. Abstract evolution equations.
    Nonlin. Anal., T.M.&A., 12, (1988), 895-919.
  50. Global existence and positivity for triangular quasilinear reaction-diffusion systems. 1989,
    unpublished manuscript
  51. Feedback stabilization of linear and semilinear parabolic systems.
    In: Semigroup Theory and Applications, Clément et al.(editors).
    Lecture Notes Pure Appl. Math. 116, 21-57, M. Dekker, New York, 1989.
  52. Parabolic evolution equations in interpolation and extrapolation spaces.
    J. Funct. Anal., 78, (1988), 233-270.
  53. Parabolic evolution equations and nonlinear boundary conditions.
    J. Diff. Equ., 72, (1988), 201-269.
  54. On abstract parabolic fundamental solutions.
    J. Math. Soc. Japan, 39, (1987), 93-116.
  55. Semigroups and nonlinear evolution equations.
    Lin. Alg. & Appl., 84, (1986), 3-32.
  56. Quasilinear parabolic systems under nonlinear boundary conditions.
    Arch. Rat. Mech. Anal., 92, (1986), 153-19
  57. Quasilinear evolution equations and parabolic systems.
    Trans. Amer. Math. Soc., 293, (1986), 191-227.
  58. Parabolic evolution equations with nonlinear boundary conditions.
    In: Nonlinear Functional Analysis and its Applications.
    F.E. Browder (editor), Proc. Symp. Pure Math. 45, Amer. Math. Soc.,Providence, R.I., 17-27, 1986.
  59. Global existence for semilinear parabolic systems.
    J. reine angew. Math., 360, (1985), 47-83.
  60. Existence and regularity for semilinear parabolic evolution equations.
    Ann. Scuola Norm. Sup. Pisa, Ser. IV, 11, (1984), 593-676.
  61. Periodic solutions of Hamiltonian systems.
    Delft Progress Report, 9, (1984), 4-18.
  62. Dual semigroups and second order linear elliptic boundary value problems.
    Israel J. Math., 45, (1983), 225-254.
  63. A note on degree theory for gradient mappings.
    Proc. Amer. Math. Soc., 85, (1982), 591-595.
  64. On the unique solvability of semi-linear operator equations in Hilbert spaces.
    J. math. pures appl., 61, (1982), 149-175.
  65. (with E. Zehnder) Multiple periodic solutions for a class of nonlinear autonomous wave equations.
    Houston J. Math., 7, (1981), 147-174.
  66. (with E. Zehnder) Periodic solutions of asymptotically linear Hamiltonian systems.
    Manuscripta Math., 32, (1980), 149-189.
  67. (with E. Zehnder) Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations.
    Ann. Scuola Norm. Sup. Pisa, Ser. IV, 7, (1980), 539-603.
  68. (with P. Hess) A multiplicity result for a class of elliptic boundary value problems.
    Proc. Royal Soc. Edinburgh, 84A,(1979), 145-151.
  69. Saddle points and multiple solutions of differential equations.
    Math. Z., 169, (1979), 127-166.
  70. (with G. Mancini) Some applications of monotone operator theory to resonance problems.
    Nonlin. Anal., T.M.&A., 3, (1979), 815-830.
  71. Order structures and fixed points.
    In: SAFA 2 - Atti del 2° Seminario di Anal. Funzionale e Appl., Cosenza,
    28. Settembre - 6. Ottobre 1977, 1-51. Università di Calabria, 1979.   pdf,
  72. (with A. Ambrosetti and G. Mancini) Elliptic equations with noninvertible Fredholm linear part and bounded nonlinearities .
    Math. Z., 158, (1978), 179-194.
  73. (with M.G. Crandall) On some existence theorems for semi-linear elliptic equations.
    Indiana Univ. Math. J., 27, (1978), 779-790.
  74. Existence and stability of solutions for semi-linear parabolic systems,
    and applications to some diffusion-reaction equations    .
    Proc. Royal Soc. Edinburgh, 81A, (1978), 35-47.
  75. Invariant sets and existence theorems for semi-linear parabolic and elliptic systems.
    J. Math. Anal. Appl., 65, (1978), 432-467.
  76. Periodic solutions of semi-linear parabolic evolution equations.
    In: Nonlinear Analysis, A Collection of Papers in Honor of Erich H. Rothe.
    L. Cesari, R. Kannan, H.F. Weinberger (editors), Academic Press, New York, 1-29, 1978.
  77. Existence and multiplicity theorems for semi-linear elliptic boundary value problems.
    Math. Z., 150, (1976), 281-295.
  78. Nonlinear eigenvalue problems having precisely two solutions.
    Math. Z., 150, (1976), 27-37.
  79. Nonlinear operators in ordered Banach spaces and some applications to nonlinear boundary value problems.
    In: Nonlinear Operators and the Calculus of Variations, Bruxelles 1975.
    Lecture Notes in Math. #543, 1-55, Springer Verlag, Berlin, 1976.
  80. Nonlinear elliptic equations with nonlinear boundary conditions.
    In: New Developments in Differential Equations, Proc. 2nd Scheveningen Conf. Diff. Equ.
    W. Eckhaus (editor), Math. Studies 21, North-Holland, Amsterdam, 43-63. 1976.
  81. Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces.
    SIAM Review, 18, (1976), 620-709.
  82. Supersolutions, monotone iterations, and stability.
    J. Diff. Equ., 21, (1976), 3
  83. (with Th. Laetsch) Positive solutions of convex nonlinear eigenvalue problems.
    Indiana Univ. Mat
  84. On the number of solutions of asymptotically superlinear two point boundary value problems.
    Arch. Rat. Mech. Anal., 55, (1974), 207-213.
  85. Multiple positive fixed points of asymptotically linear maps.
    J. Funct. Anal., 17, (1974),
  86. Fixed points of asymptotically linear maps in ordered Banach spaces.
    J. Funct. Anal., 14, (1973), 162-171.
  87. (with S. Weiss) On the uniqueness of the topological degree.
    Math. Z., 130, (1973), 39-54.
  88. Existence theorems for equations of Hammerstein type.
    Applicable Anal., 2, (1973), 385-397.
  89. On the number of solutions of nonlinear equations in ordered Banach spaces.
    J. Funct. Anal., 11, (1972), 346-384.
  90. Existence of multiple solutions for nonlinear elliptic boundary value problems.
    Indiana Univ. Math. J., 21, (1972), 925-935.
  91. Lusternik-Schnirelman theory and nonlinear eigenvalue problems.
    Math. Ann., 199, (1972), 55-72.
  92. A uniqueness theorem for nonlinear elliptic boundary value problems.
    Arch. Rat. Mech. Anal., 44, (1972), 178-181.
  93. Über die näherungsweise Lösung nichtlinearer Integralgleichungen.
    Numerische Mathematik, 19, (1972), 29-45
  94. On the existence of positive solutions of nonlinear elliptic boundary value problems.
    Indiana Univ. Math. J., 21, (1971), 12
  95. Über die Konvergenzgeschwindigkeit des Galerkin-Verfahrens für Hammersteinsche Gleichungen.
    Arch. Rat. Mech. Anal., 37, (1970), 33-47.
  96. Hammersteinsche Gleichungen mit kompakten Kernen.
    Math. Ann., 186, (1970), 334-340.
  97. Zum Galerkin-Verfahren für die Hammersteinsche Gleichung.
    Arch. Rat. Mech. Anal., 35, (1969), 114-121.
  98. Über die Existenz und Eindeutigkeit einer Lösung der Hammersteinschen Gleichung in Banachräumen.
    J. Math. Mech., 19, (1969), 143-154.
  99. Ein Existenz und Eindeutigkeitssatz für die Hammersteinsche Gleichung in Banachräumen.
    Math. Z., 111, (1969), 175-190.
  100. Ein Iterationsverfahren für eine von C.L. Dolph betrachtete Klasse von Gleichungen Hammersteinschen Typs.
    ZAMM, 48, (1968), T50-T53.
  101. Über die Existenz und iterative Berechnung einer Lösung der Hammersteinschen Gleichung.
    Aequationes math., 1, (1968), 242-266.
  102. Monte-Carlo-Methoden und lineare Randwertprobleme.
    ZAMM, 48, (1968), 109-115.
  103. Der Rechenaufwand bei der Monte-Carlo-Methode mit Informationsspeicherung.
    ZAMM, 48, (1968), 128-131.
  104. Optimale Anfangsverteilungen bei der Monte-Carlo-Methode mit Informationsspeicherung.
    ZAMM, 47, (1967), 285-299.
  105. Eine Monte-Carlo-Methode mit Informationsspeicherung zur Lösung von elliptischen Randwertproblemen.
    Z. Wahrscheinlichkeitstheorie verw. Gebiete, 8, (1967), 117-130.

 

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