Free Access
Issue
ESAIM: COCV
Volume 10, Number 1, January 2004
Page(s) 28 - 52
DOI https://doi.org/10.1051/cocv:2003035
Published online 15 February 2004
  1. W. Allegretto and Yin Xi Huang, A Picone's identity for the p-Laplacian and applications. Nonlin. Anal. TMA 32 (1998) 819-830. [CrossRef] [Google Scholar]
  2. A. Alvino, V. Ferone, G. Trombetti and P.L. Lions, Convex symmetrization and applications. Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997) 275-293. [CrossRef] [MathSciNet] [Google Scholar]
  3. A. Anane, Simplicité et isolation de la première valeur propre du p-laplacien avec poids. C. R. Acad. Sci. Paris Sér. I Math. 305 (1987) 725-728. [Google Scholar]
  4. A. Anane, A. Benazzi and O. Chakrone, Sur le spectre d'un opérateur quasilininéaire elliptique "dégénéré". Proyecciones 19 (2000) 227-248. [MathSciNet] [Google Scholar]
  5. G. Aronsson, Extension of functions satisfying Lipschitz conditions. Ark. Math. 6 (1967) 551-561. [CrossRef] [MathSciNet] [Google Scholar]
  6. G. Aronsson, On the partial differential equation Formula . Ark. Math. 7 (1968) 395-425. [CrossRef] [Google Scholar]
  7. G. Barles, Remarks on uniqueness results of the first eigenvalue of the p-Laplacian. Ann. Fac. Sci. Toulouse 9 (1988) 65-75. [Google Scholar]
  8. G. Barles and J. Busca, Existence and comparison results for fully nonlinear degenerate elliptic equations without zeroth-order term. Comm. Partial Differential Equations 26 (2001) 2323-2337. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Belloni and B. Kawohl, A direct uniqueness proof for equations involving the p-Laplace operator. Manuscripta Math. 109 (2002) 229-231. [CrossRef] [MathSciNet] [Google Scholar]
  10. T. Bhattacharya, E. DiBenedetto and J. Manfredi, Limits as p → ∞ of Δpup = ƒ and related extremal problems. Rend. Sem. Mat., Fasciolo Speciale Nonlinear PDE's. Univ. Torino (1989) 15-68. [Google Scholar]
  11. T. Bhattacharya, An elementary proof of the Harnack inequality for non-negative infinity-superharmonic functions. Electron. J. Differential Equations 2001 (2001) 1-8. [Google Scholar]
  12. H. Brezis and L.Oswald, Remarks on sublinear problems. Nonlinear Anal. 10 (1986) 55-64. [CrossRef] [MathSciNet] [Google Scholar]
  13. M.G. Crandall, L.C. Evans and R.F. Gariepy, Optimal Lipschitz extensions and the infinity Laplacian. Calc. Var. Partial Differential Equations 13 (2001) 123-139. [MathSciNet] [Google Scholar]
  14. M.G. Crandall, H. Ishii and P.L. Lions, User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. (N.S.) 27 (1992) 1-67. [CrossRef] [MathSciNet] [Google Scholar]
  15. Y.G. Chen, Y. Giga and S. Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations. J. Differ. Geom. 33 (1991) 749-786. [Google Scholar]
  16. J.I. Diaz and J.E. Saá, Existence et unicité de solutions positives pour certaines équations elliptiques quasilinéaires. C. R. Acad. Sci. Paris Sér. I Math. 305 (1987) 521-524. [Google Scholar]
  17. E. DiBenedetto, C1+α local regularity of weak solutions of degenerate elliptic equations. Nonlinear Anal. TMA 7 (1983) 827-850. [CrossRef] [MathSciNet] [Google Scholar]
  18. A. Elbert, A half-linear second order differential equation. Qualitative theory of differential equations, (Szeged 1979). Colloq. Math. Soc. János Bolyai 30 (1981) 153-180. [Google Scholar]
  19. N. Fukagai, M. Ito and K. Narukawa, Limit as p → ∞ of p-Laplace eigenvalue problems and L inequality of the Poincaré type. Differ. Integral Equations 12 (1999) 183-206. [Google Scholar]
  20. M. Giaquinta and E. Giusti, On the regularity of the minima of variational integrals. Acta Math. 148 (1982) 31-46. [CrossRef] [MathSciNet] [Google Scholar]
  21. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of second Order. Springer Verlag, Berlin-Heidelberg-New York (1977). [Google Scholar]
  22. T. Ishibashi and S. Koike, On fully nonlinear pdes derived from variational problems of Lp-norms. SIAM J. Math. Anal. 33 (2001) 545-569. [CrossRef] [MathSciNet] [Google Scholar]
  23. U. Janfalk, Behaviour in the limit, as p → ∞, of minimizers of functionals involving p-Dirichlet integrals. SIAM J. Math. Anal. 27 (1996) 341-360. [CrossRef] [MathSciNet] [Google Scholar]
  24. R. Jensen, Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient. Arch. Rational Mech. Anal. 123 (1993) 51-74. [CrossRef] [MathSciNet] [Google Scholar]
  25. P. Juutinen, Personal Communications. [Google Scholar]
  26. P. Juutinen, P. Lindqvist and J. Manfredi, The ∞-eigenvalue problem. Arch. Rational Mech. Anal. 148 (1999) 89-105. [CrossRef] [MathSciNet] [Google Scholar]
  27. B. Kawohl, Rearrangements and convexity of level sets in PDE. Springer, Lecture Notes in Math. 1150 (1985). [Google Scholar]
  28. B. Kawohl, A family of torsional creep problems. J. Reine Angew. Math. 410 (1990) 1-22. [CrossRef] [MathSciNet] [Google Scholar]
  29. B. Kawohl, Symmetry results for functions yielding best constants in Sobolev-type inequalities. Discrete Contin. Dynam. Systems 6 (2000) 683-690. [CrossRef] [MathSciNet] [Google Scholar]
  30. B. Kawohl and N. Kutev, Viscosity solutions for degenerate and nonmonotone elliptic equations, edited by B. da Vega, A. Sequeira and J. Videman. Plenum Press, New York & London, Appl. Nonlinear Anal. (1999) 185-210. [Google Scholar]
  31. O.A. Ladyzhenskaya and N.N. Ural'tseva, Linear and quasilinear equations of elliptic type,Second edition, revised. Izdat. “Nauka” Moscow (1973). English translation by Academic Press. [Google Scholar]
  32. G.M. Lieberman, Gradient estimates for a new class of degenerate elliptic and parabolic equations. Ann. Scuola Normale Superiore Pisa Ser. IV 21 (1994) 497-522. [Google Scholar]
  33. P. Lindqvist, A nonlinear eigenvalue problem. Rocky Mountain J. 23 (1993) 281-288. [CrossRef] [MathSciNet] [Google Scholar]
  34. P. Lindqvist, On the equation divFormula =0. Proc. Amer. Math. Soc. 109 (1990) 157-164 . [MathSciNet] [Google Scholar]
  35. P. Lindqvist, Addendum to "On the equation divFormula =0". Proc. Amer. Math. Soc. 116 (1992) 583-584. [MathSciNet] [Google Scholar]
  36. P. Lindqvist, Some remarkable sine and cosine functions. Ricerche Mat. 44(1995) 269-290. [MathSciNet] [Google Scholar]
  37. J.L. Lions, Quelques méthodes de résolutions des problèmes aux limites non linéaires. Dunod, Gauthier-Villars, Paris (1969). [Google Scholar]
  38. M. Ohnuma and K. Sato, Singular degenerate parabolic equations with applications to the p-Laplace diffusion equation. Comm. Partial Differential Equations 22 (1997) 381-411. [MathSciNet] [Google Scholar]
  39. M. Ôtani, Existence and nonexistence of nontrivial solutions of some nonlinear degenerate elliptic equations. J. Funct. Anal. 76 (1988) 140-159. [CrossRef] [MathSciNet] [Google Scholar]
  40. S. Sakaguchi, Concavity properties of solutions to some degenerate quasilinear elliptic Dirichlet problems. Ann. Scuola Normale Superiore Pisa 14 (1987) 404-421. [Google Scholar]
  41. G. Talenti, Personal Communication, letter dated Oct. 15, 2001 [Google Scholar]
  42. P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations. J. Differential Equations 51 (1984) 126-150. [CrossRef] [MathSciNet] [Google Scholar]
  43. N. Trudinger, On Harnack type inequalities and their application to quasilinear elliptic equations. Comm. Pure Appl. Math. 20 (1967) 721-747. [CrossRef] [MathSciNet] [Google Scholar]
  44. N.N. Ural'tseva and A.B. Urdaletova, The boundedness of the gradients of generalized solutions of degenerate quasilinear nonuniformly elliptic equations. Vestnik Leningrad Univ. Math. 16 (1984) 263-270. [Google Scholar]
  45. I.M. Višik, Sur la résolutions des problèmes aux limites pour des équations paraboliques quasi-linèaires d'ordre quelconque. Mat. Sbornik 59 (1962) 289-325. [Google Scholar]
  46. I.M. Višik, Quasilinear strongly elliptic systems of differential equations in divergence form. Trans. Moscow. Math. Soc. 12 (1963) 140-208; Translation from Tr. Mosk. Mat. Obs. 12 (1963) 125-184. [Google Scholar]

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