Existence and nonexistence results for anisotropic quasilinear elliptic equations
Fragalà, Ilaria ; Gazzola, Filippo ; Kawohl, Bernd
Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004), p. 715-734 / Harvested from Numdam
@article{AIHPC_2004__21_5_715_0,
     author = {Fragal\`a, Ilaria and Gazzola, Filippo and Kawohl, Bernd},
     title = {Existence and nonexistence results for anisotropic quasilinear elliptic equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {21},
     year = {2004},
     pages = {715-734},
     doi = {10.1016/j.anihpc.2003.12.001},
     mrnumber = {2086756},
     zbl = {02116186},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2004__21_5_715_0}
}
Fragalà, Ilaria; Gazzola, Filippo; Kawohl, Bernd. Existence and nonexistence results for anisotropic quasilinear elliptic equations. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) pp. 715-734. doi : 10.1016/j.anihpc.2003.12.001. http://gdmltest.u-ga.fr/item/AIHPC_2004__21_5_715_0/

[1] Acerbi E., Fusco N., Partial regularity under anisotropic (p,q) growth conditions, J. Differential Equations 107 (1994) 46-67. | MR 1260848 | Zbl 0807.49010

[2] Ambrosetti A., Rabinowitz P.H., Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973) 349-381. | MR 370183 | Zbl 0273.49063

[3] Belloni M., Kawohl B., The pseudo-p-Laplace eigenvalue problem and viscosity solutions as p→∞, ESAIM COCV 10 (2004) 28-52. | Numdam | Zbl 1092.35074

[4] Brezis H., Kato T., Remarks on the Schrödinger operator with singular complex potentials, J. Math. Pures Appl. 58 (1979) 137-151. | MR 539217 | Zbl 0408.35025

[5] Cianchi A., Local boundedness of minimizers of anisotropic functionals, Ann. Inst. H. Poincaré ANL 17 (2000) 147-168. | Numdam | MR 1753091 | Zbl 0984.49019

[6] Dal Maso G., Murat F., Almost everywhere convergence of gradients of solutions to nonlinear elliptic systems, Nonlinear Anal. TMA 31 (1998) 405-412. | MR 1487552 | Zbl 0890.35039

[7] Degiovanni M., Musesti A., Squassina M., On the regularity of solutions in the Pucci-Serrin identity, Calc. Var. Partial Differential Equations 18 (2003) 317-334. | MR 2018671 | Zbl 1046.35039

[8] Egnell H., Existence and nonexistence results for m-Laplace equations involving critical Sobolev exponents, Arch. Rational Mech. Anal. 104 (1988) 57-77. | MR 956567 | Zbl 0675.35036

[9] Gazzola F., Critical exponents which relate embedding inequalities with quasilinear elliptic problems, in: Proc. 4th Int. Conf. Dyn. Syst. Diff. Eq., Wilmington, 2002, pp. 327-335. | MR 2018132 | Zbl 02046199

[10] Giaquinta M., Growth conditions and regularity, a counterexample, Manuscripta Math. 59 (1987) 245-248. | MR 905200 | Zbl 0638.49005

[11] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 2001. | MR 1814364 | Zbl 1042.35002

[12] Guedda M., Veron L., Quasilinear elliptic equations involving critical Sobolev exponents, Nonlinear Anal. TMA 13 (1989) 879-902. | MR 1009077 | Zbl 0714.35032

[13] Kolodii I.M., An estimate of the maximum of the modulus of generalized solutions of the Dirichlet problem, for elliptic equations of divergent form, Ukrainian Math. J. 47 (1995) 733-748. | MR 1356907 | Zbl 0937.35063

[14] Kruzhkov S.N., Kolodii I.M., On the theory of embedding of anisotropic Sobolev spaces, Russian Math. Surveys 38 (1983) 188-189. | MR 695478 | Zbl 0534.46022

[15] Ladyzhenskaya O.A., Ural'Tseva N.N., Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. | MR 244627 | Zbl 0164.13002

[16] Lieberman G.M., Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal. TMA 12 (1988) 1203-1219. | MR 969499 | Zbl 0675.35042

[17] Lieberman G.M., Gradient estimates for a new class of degenerate elliptic and parabolic equations, Ann. Sc. Norm. Sup. Pisa 21 (1994) 497-522. | Numdam | MR 1318770 | Zbl 0839.35018

[18] Marcellini P., Regularity and existence of solutions of elliptic equations with p,q-growth conditions, J. Differential Equations 90 (1991) 1-30. | MR 1094446 | Zbl 0724.35043

[19] Nikol'Skii S.M., On imbedding, continuation and approximation theorems for differentiable functions of several variables, Russian Math. Surv. 16 (1961) 55-104. | MR 149267 | Zbl 0117.29101

[20] Otani M., Existence and nonexistence of nontrivial solutions of some nonlinear degenerate elliptic equations, J. Funct. Anal. 76 (1988) 140-159. | MR 923049 | Zbl 0662.35047

[21] Pohožaev S.J., Eigenfunctions of the equation Δu+λf(u)=0, Soviet Math. Dokl. 6 (1965) 1408-1411.

[22] Pohožaev S.J., On the eigenfunction of quasilinear elliptic equations, Math. USSR Sbornik 11 (1970) 171-188.

[23] Pucci P., Serrin J., A general variational identity, Indiana Univ. Math. J. 35 (1986) 681-703. | MR 855181 | Zbl 0625.35027

[24] Rákosnik J., Some remarks to anisotropic Sobolev spaces I, Beiträge zur Analysis 13 (1979) 55-68. | MR 536217 | Zbl 0399.46025

[25] Rákosnik J., Some remarks to anisotropic Sobolev spaces II, Beiträge zur Analysis 15 (1981) 127-140. | MR 614784 | Zbl 0494.46034

[26] Tolksdorf P., On the Dirichlet problem for quasilinear equations in domains with conical boundary points, Comm. Partial Differential Equations 8 (1983) 773-817. | MR 700735 | Zbl 0515.35024

[27] Troisi M., Teoremi di inclusione per spazi di Sobolev non isotropi, Ricerche Mat. 18 (1969) 3-24. | MR 415302 | Zbl 0182.16802

[28] Ural'Tseva N.N., Urdaletova A.B., The boundedness of the gradients of generalized solutions of degenerate quasilinear nonuniformly elliptic equations, Vestnik Leningrad Univ. Math. 16 (1984) 263-270. | Zbl 0569.35029

[29] Ven'-Tuan L., On embedding theorems for spaces of functions with partial derivatives of various degrees of summability, Vestnik Leningrad Univ. 16 (1961) 23-37, (in Russian). | MR 143020 | Zbl 0100.31803