Nonexistence of local solutions to semilinear partial differential inequalities
Pohozaev, Stanislav I ; Tesei, Alberto
Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004), p. 487-502 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_2004__21_4_487_0,
     author = {Pohozaev, Stanislav I and Tesei, Alberto},
     title = {Nonexistence of local solutions to semilinear partial differential inequalities},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {21},
     year = {2004},
     pages = {487-502},
     doi = {10.1016/j.anihpc.2003.06.002},
     mrnumber = {2069634},
     zbl = {1064.35220},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2004__21_4_487_0}
}

Pohozaev, Stanislav I; Tesei, Alberto. Nonexistence of local solutions to semilinear partial differential inequalities. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) pp. 487-502. doi : 10.1016/j.anihpc.2003.06.002. http://gdmltest.u-ga.fr/item/AIHPC_2004__21_4_487_0/

[1] Brezis H, Cabré X, Some simple nonlinear PDE's without solutions, Boll. Un. Mat. Ital. 1-B (1998) 223-262. | MR 1638143 | Zbl 0907.35048

[2] Brezis H, Cazenave T, Martel Y, Ramiandrisoa A, Blow up for ut−Δu=g(u) revisited, Adv. Differential Equations 1 (1996) 73-90. | Zbl 0855.35063

[3] Brezis H, Vazquez J.L, Blow-up solutions of some nonlinear elliptic problems, Rev. Mat. Univ. Compl. Madrid 10 (1997) 443-469. | MR 1605678 | Zbl 0894.35038

[4] Cabré X, Martel Y, Weak eigenfunctions for the linearization of extremal elliptic problems, J. Funct. Anal. 156 (1998) 30-56. | MR 1632972 | Zbl 0908.35044

[5] Cabré X, Martel Y, Existence versus explosion instantanée pour des equations de la chaleur linéaires avec potentiel singulier, C. R. Acad. Sci. Paris 329 (1999) 973-978. | MR 1733904 | Zbl 0940.35105

[6] Caffarelli L, Gidas B, Spruck J, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math. 42 (1989) 271-297. | MR 982351 | Zbl 0702.35085

[7] Dautray R, Lions J.L, Mathematical Analysis and Numerical Methods for Science and Technology, vol. I, Springer, 1985. | Zbl 0683.35001

[8] Galakhov E, Some nonexistence results for quasilinear elliptic problems, J. Math. Anal. Appl. 252 (2000) 256-277. | MR 1797855 | Zbl 0970.35070

[9] Dupaigne L, A nonlinear elliptic PDE with the inverse square potential, J. Anal. Math. 86 (2002) 359-398. | MR 1894489 | Zbl 1034.35043

[10] Gidas B, Spruck J, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math. 34 (1981) 525-598. | MR 615628 | Zbl 0465.35003

[11] Holcman D, Nonlinear PDE with vector fields, J. Anal. Math. 81 (2000) 111-137. | MR 1785279 | Zbl 0963.35054

[12] Joseph D.D, Lundgren T.S, Quasilinear Dirichlet problems driven by positive sources, Arch. Rat. Mech. Anal. 49 (1973) 241-269. | MR 340701 | Zbl 0266.34021

[13] Korevaar N, Mazzeo R, Pacard F, Schoen R, Refined asymptotics for constant scalar curvature metrics with isolated singularities, Invent. Math. 135 (1989) 233-272. | MR 1666838 | Zbl 0958.53032

[14] Mitidieri E, Pohozaev S.I, The absence of global positive solutions to quasilinear elliptic inequalities, Dokl. Russ. Acad. Sci. 359 (1998) 456-460. | MR 1668404 | Zbl 0976.35100

[15] Mitidieri E, Pohozaev S.I, A Priori Estimates and Blow-Up of Solutions to Nonlinear Partial Differential Equations and Inequalities, Proc. Steklov Inst. Math., vol. 234, International Academic Publishing, Moscow, 2001. | MR 1879326 | Zbl 1074.35500

[16] Moschini L, Pohozaev S.I, Tesei A, Existence and nonexistence of solutions of nonlinear Dirichlet problems, J. Funct. Anal. 177 (2000) 365-382. | MR 1795956 | Zbl 0976.35025

[17] Moschini L, Pohozaev S.I, Tesei A, On a class of nonlinear Dirichlet problems with first order terms, in: International Conference on Differential and Functional Differential Equations, Moscow, 1999, Funct. Differ. Equations 8 (2001) 345-352. | MR 1950978 | Zbl 1098.35555

[18] Pohozaev S.I, Tesei A, Blow-up of nonnegative solutions to quasilinear parabolic inequalities, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 11 (2000) 99-109. | MR 1797514 | Zbl 1007.35003

[19] Pohozaev S.I, Tesei A, Instantaneous blow-up of solutions to a class of hyperbolic inequalities, Electronic J. Differential Equations Conference 08 (2002) 155-165. | Zbl 1024.35081

[20] Serrin J, Local behavior of solutions of quasi-linear equations, Acta Math. 111 (1964) 247-302. | MR 170096 | Zbl 0128.09101

[21] Smets D, Tesei A, On a class of semilinear elliptic problems with first order terms, Adv. Differential Equations 8 (2003) 257-278. | MR 1948046 | Zbl 02002530

[22] Terracini S, On positive solutions to a class of equations with singular coefficient and critical exponent, Adv. Differential Equations 1 (1996) 241-264. | MR 1364003 | Zbl 0847.35045

[23] Vazquez J.L, Zuazua E, The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential, J. Funct. Anal. 173 (2000) 103-153. | MR 1760280 | Zbl 0953.35053