Free Access
Volume 10, Number 1, January 2004
Page(s) 28 - 52
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]
  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]
  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.
  4. A. Anane, A. Benazzi and O. Chakrone, Sur le spectre d'un opérateur quasilininéaire elliptique "dégénéré". Proyecciones 19 (2000) 227-248. [MathSciNet]
  5. G. Aronsson, Extension of functions satisfying Lipschitz conditions. Ark. Math. 6 (1967) 551-561. [CrossRef] [MathSciNet]
  6. G. Aronsson, On the partial differential equation Formula . Ark. Math. 7 (1968) 395-425. [CrossRef]
  7. G. Barles, Remarks on uniqueness results of the first eigenvalue of the p-Laplacian. Ann. Fac. Sci. Toulouse 9 (1988) 65-75.
  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]
  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]
  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.
  11. T. Bhattacharya, An elementary proof of the Harnack inequality for non-negative infinity-superharmonic functions. Electron. J. Differential Equations 2001 (2001) 1-8.
  12. H. Brezis and L.Oswald, Remarks on sublinear problems. Nonlinear Anal. 10 (1986) 55-64. [CrossRef] [MathSciNet]
  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]
  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]
  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.
  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.
  17. E. DiBenedetto, C1+α local regularity of weak solutions of degenerate elliptic equations. Nonlinear Anal. TMA 7 (1983) 827-850. [CrossRef] [MathSciNet]
  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.
  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.
  20. M. Giaquinta and E. Giusti, On the regularity of the minima of variational integrals. Acta Math. 148 (1982) 31-46. [CrossRef] [MathSciNet]
  21. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of second Order. Springer Verlag, Berlin-Heidelberg-New York (1977).
  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]
  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]
  24. R. Jensen, Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient. Arch. Rational Mech. Anal. 123 (1993) 51-74. [CrossRef] [MathSciNet]
  25. P. Juutinen, Personal Communications.
  26. P. Juutinen, P. Lindqvist and J. Manfredi, The ∞-eigenvalue problem. Arch. Rational Mech. Anal. 148 (1999) 89-105. [CrossRef] [MathSciNet]
  27. B. Kawohl, Rearrangements and convexity of level sets in PDE. Springer, Lecture Notes in Math. 1150 (1985).
  28. B. Kawohl, A family of torsional creep problems. J. Reine Angew. Math. 410 (1990) 1-22. [CrossRef] [MathSciNet]
  29. B. Kawohl, Symmetry results for functions yielding best constants in Sobolev-type inequalities. Discrete Contin. Dynam. Systems 6 (2000) 683-690. [CrossRef] [MathSciNet]
  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.
  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.
  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.
  33. P. Lindqvist, A nonlinear eigenvalue problem. Rocky Mountain J. 23 (1993) 281-288. [CrossRef] [MathSciNet]
  34. P. Lindqvist, On the equation divFormula =0. Proc. Amer. Math. Soc. 109 (1990) 157-164 . [MathSciNet]
  35. P. Lindqvist, Addendum to "On the equation divFormula =0". Proc. Amer. Math. Soc. 116 (1992) 583-584. [MathSciNet]
  36. P. Lindqvist, Some remarkable sine and cosine functions. Ricerche Mat. 44(1995) 269-290. [MathSciNet]
  37. J.L. Lions, Quelques méthodes de résolutions des problèmes aux limites non linéaires. Dunod, Gauthier-Villars, Paris (1969).
  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]
  39. M. Ôtani, Existence and nonexistence of nontrivial solutions of some nonlinear degenerate elliptic equations. J. Funct. Anal. 76 (1988) 140-159. [CrossRef] [MathSciNet]
  40. S. Sakaguchi, Concavity properties of solutions to some degenerate quasilinear elliptic Dirichlet problems. Ann. Scuola Normale Superiore Pisa 14 (1987) 404-421.
  41. G. Talenti, Personal Communication, letter dated Oct. 15, 2001
  42. P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations. J. Differential Equations 51 (1984) 126-150. [CrossRef] [MathSciNet]
  43. N. Trudinger, On Harnack type inequalities and their application to quasilinear elliptic equations. Comm. Pure Appl. Math. 20 (1967) 721-747. [CrossRef] [MathSciNet]
  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.
  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.
  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.

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.