Concavity properties of solutions to some degenerate quasilinear elliptic Dirichlet problems

Shigeru Sakaguchi

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1987)

  • Volume: 14, Issue: 3, page 403-421
  • ISSN: 0391-173X

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Sakaguchi, Shigeru. "Concavity properties of solutions to some degenerate quasilinear elliptic Dirichlet problems." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 14.3 (1987): 403-421. <http://eudml.org/doc/84012>.

@article{Sakaguchi1987,
author = {Sakaguchi, Shigeru},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {concavity; nonlinear degenerate p-Laplacian; Poincaré constant; zero Dirichlet boundary condition},
language = {eng},
number = {3},
pages = {403-421},
publisher = {Scuola normale superiore},
title = {Concavity properties of solutions to some degenerate quasilinear elliptic Dirichlet problems},
url = {http://eudml.org/doc/84012},
volume = {14},
year = {1987},
}

TY - JOUR
AU - Sakaguchi, Shigeru
TI - Concavity properties of solutions to some degenerate quasilinear elliptic Dirichlet problems
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1987
PB - Scuola normale superiore
VL - 14
IS - 3
SP - 403
EP - 421
LA - eng
KW - concavity; nonlinear degenerate p-Laplacian; Poincaré constant; zero Dirichlet boundary condition
UR - http://eudml.org/doc/84012
ER -

References

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  1. [1] T. Aubin, Nonlinear Analysis on Manifolds. Monge-Ampère Equations, Springer-Verlag, New YorkHeidelbergBerlin, 1982. Zbl0512.53044MR681859
  2. [2] M.S. Berger, Nonlinearity And Functional Analysis Lectures on Nonlinear Problems in Mathematical Analysis, Academic Press, New YorkSan FranciscoLondon, 1977. Zbl0368.47001MR488101
  3. [3] H.J. Brascamp and E.H. Lieb, On extension of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation, J. Funct. Anal.22 (1976), 366-389. Zbl0334.26009MR450480
  4. [4] L.A. Caffarelli and A. Friedman, Convexity of solutions of semilinear elliptic equations, Duke Math. J.52 (1985), 431-456. Zbl0599.35065MR792181
  5. [5] L.A Caffarelli and J. Spruck, Convexity properties of solutions to some classical varational problems, Comm. P. D. E.7 (1982), 1337-1379. Zbl0508.49013MR678504
  6. [6] J.I. Díaz, Nonlinear partial differential equations and free boundaries volume I Elliptic equations, Research Notes in Mathematics106, Pitman Advanced Publishing Program, Boston-London-Melbourne, 1985. Zbl0595.35100MR853732
  7. [7] M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Annals of Mathematics Studies Number 105, Princeton University Press, Princeton, New Jersey, 1983. Zbl0516.49003MR717034
  8. [8] M. Giaquinta and E. Giusti, On the regularity of the minima of variational integrals, Acta Math.148 (1982), 31-46. Zbl0494.49031MR666107
  9. [9] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin-Heidelberg -New York, 1977. Zbl0361.35003MR473443
  10. [10] B. Kawohl, When are solutions to nonlinear elliptic boundary value problems convex?, Comm. P. D. E.10 (1985), 1213-1225. Zbl0587.35026MR806439
  11. [11] B. Kawohl, A remark on N. Korevaar's concavity maximum principle and on the asymptotic uniqueness of solutions to the plasma problem, Math. Methods Appl. Sci.8 (1986), 93-101. Zbl0616.35006MR833253
  12. [12] B. Kawohl, When are superharmonic functions concave? Applications to the St. Venant torsion problem and to the fundamental mode of the clamped membrane, Z. Angew. Math. Mech.64 (1984), 364-366. Zbl0581.73006MR754534
  13. [13] A.U. Kennington, Power concavity and boundary value problems, Indiana Univ. Math. J.34 (1985), 687-704. Zbl0549.35025MR794582
  14. [14] N. Korevaar, Capillary surface convexity above convex domains, Indiana Univ. Math. J.32 (1983), 73-81. Zbl0481.35023MR684757
  15. [15] N. Korevaar, Convex solutions to nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math. J.32 (1983), 603-614. Zbl0481.35024MR703287
  16. [16] N. Korevaar, and J.L. Lewis, Convex solutions of certain elliptic equations have constant rank Hessians, Arch. Rational Mech. Anal.97 (1987), 19-32. Zbl0624.35031MR856307
  17. [17] O.A. Ladyzhenskaya and N.N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York. and London, 1968. Zbl0164.13002MR244627
  18. [18] J.L. Lewis, Capacitary functions in convex rings, Arch. Rational Mech. Anal., 66 (1977), 201- 224. Zbl0393.46028MR477094
  19. [19] F. Riesz and B. Sz-Nagy, Functional Analysis, Translated from the 2nd French edition by Leo F. Boron, Frederick Ungar Publishing Co., New York1955. Zbl0070.10902MR71727
  20. [20] F. de Thelin, Sur l'espace propre associé à la première valeur propre du pseudo-Laplacien, C.R. Acad. Sc. Paris, Sér. A303 (1986), 355-358. Zbl0598.35045MR860838
  21. [21] P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, J. Diff. Equations51 (1984), 126-150. Zbl0488.35017MR727034
  22. [22] P. Tolksdorf, On the Dirichlet problem for quasilinear equations in domains with conical boundary points, Comm. P. D. E.8 (1983), 773-817. Zbl0515.35024MR700735
  23. [23] N.S. Trudinger, On Harnack type inequalities and their application to quasilinear elliptic equations, Comm. Pure Appl. Math.20 (1967), 721-747. Zbl0153.42703MR226198

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