Hardy Inequalities and Some Critical Elliptic and Parabolic Problems

Journal of Differential Equations - Tập 144 - Trang 441-476 - 1998
J.P. Garcı́a Azorero1, I. Peral Alonso1
1Departamento de Matemáticas, U.A.M. 28049, Madrid, Spain

Tài liệu tham khảo

J. A. Aguilar, I. Peral, On some nonlinear parabolic equations Ambrosetti, 1973, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14, 349, 10.1016/0022-1236(73)90051-7 Ambrosetti, 1996, Multiplicity of solutions for semilinear and quasi-linear elliptic problems, J. Funct. Anal., 137, 219, 10.1006/jfan.1996.0045 Arioli, 1996, Some results onp, Research Report in Mathematics Baras, 1984, The heat equation with a singular potential, Trans. Amer. Math. Soc., 294, 121, 10.1090/S0002-9947-1984-0742415-3 Bénilan, 1995, XXII Boccardo, 1992, Nonlinear elliptic equations with right hand side measures, Comm. Partial Differential Equations, 17, 641, 10.1080/03605309208820857 Boccardo, 1992, Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations, Nonlinear Anal., 19, 581, 10.1016/0362-546X(92)90023-8 Brezis, 1983, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math., 36, 437, 10.1002/cpa.3160360405 Dacorogna, 1989 De Giorgi, 1968 Di Benedetto, 1993 del Pino, 1989, A homotopic deformation alongpupu1fxuuuTp, J. Diff. Equations, 80, 1, 10.1016/0022-0396(89)90093-4 Ekeland, 1974, On the variational principle, J. Math. Anal. Appl., 47, 324, 10.1016/0022-247X(74)90025-0 Fefferman, 1983, The uncertainty principle, Bull. Amer. Math. Soc., 9, 129, 10.1090/S0273-0979-1983-15154-6 Fujita, 1968, On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations, Proc. Sympos. Pure Math., 18, 138 Galaktionov, 1997, Continuation of blow-up solutions of nonlinear heat equations in several space dimensions, Comm. Pure Appl. Math., 50, 1, 10.1002/(SICI)1097-0312(199701)50:1<1::AID-CPA1>3.0.CO;2-H Garcia Azorero, 1991, Multiplicity of solutions for elliptic problems with critical exponent or with a non-symmetric term, Trans. Amer. Math. Soc., 323, 877, 10.1090/S0002-9947-1991-1083144-2 Gelfand, 1963, Some problems in the theory of quasilinear equations, Amer. Math. Soc. Ser. 2, 29, 295 Guedda, 1989, Quasilinear elliptic equations involving critical exponents, Nonlinear Anal., 13, 879, 10.1016/0362-546X(89)90020-5 Hardy, 1934 Lions, 1985, The concentration-compactness principle in the calculus of variations. The limit case. Part I, Rev. Mat. Iberomaricana, 1, 145, 10.4171/RMI/6 Merle, 1991, Positive solutions of elliptic equations involving supercritical growth, Proc. Royal Soc. Edinburgh A, 118, 49, 10.1017/S0308210500028882 Peral, 1995, On the stability or instability of the singular solution of the semilinear heat equation with exponential term, Arch. Rational Mech. Anal., 129, 201, 10.1007/BF00383673 Pohozaev, 1970, On the eigenfunctions of quasilinear elliptic problems, Mat. Sbornik, 82, 171, 10.1070/SM1970v011n02ABEH001133 Pucci, 1986, A general variational identity, Indiana University Math. J., 35, 681, 10.1512/iumj.1986.35.35036 Rabinowitz, 1975 Serrin, 1959, On a fundamental theorem of the calculus of variations, Acta Math., 102, 1, 10.1007/BF02559565 Tonelli, 1921