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Nonexistence results for a fully nonlinear evolution inequality
1. | School of Science, Hezhou University, Hezhou, 542899, Guangxi Province, China |
References:
[1] |
L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equations. III. Functions of the eigenvalues of the Hessian, Acta Math., 155 (1985), 261-301.
doi: 10.1007/BF02392544. |
[2] |
H. Fujita, On the blowing up of solutions of the Cauchy problems for $u_t=\Delta u + u^{1+\alpha}$, J. Fac. Sci. Univ. Tokyo, Sect. I, 13 (1966), 109-124. |
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K. Hayakawa, On the nonexistence of global solutions of some semilinear parabolic equations, Proc. Japan Acad., 49 (1973), 503-505.
doi: 10.3792/pja/1195519254. |
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D. Labutin, Potential estimates for a class of fully nonlinear elliptic equations, Duke Math. J., 111 (2002), 1-49.
doi: 10.1215/S0012-7094-02-11111-9. |
[5] |
E. Mitidieri and S. Pohozaev, Towards a unified approach to nonexistence of solutions for a class of differential inequalities, Milan J. Math., 72 (2004), 129-162.
doi: 10.1007/s00032-004-0032-7. |
[6] |
Q. Ou, Nonexistence results for Hessian inequality, Methods Appl. Anal., 17 (2010), 213-223.
doi: 10.4310/MAA.2010.v17.n2.a5. |
[7] |
N. C. Phuc and I. E. Verbitsky, Quasilinear and Hessian equations of Lane-Emden type, Ann. of Math., 168 (2008), 859-914.
doi: 10.4007/annals.2008.168.859. |
[8] |
N. C. Phuc and I. E. Verbitsky, Local integral estimates and removable singularities for quasilinear and Hessian equations with nonlinear source terms, Comm. Partial Differential Equations, 31 (2006), 1779-1791.
doi: 10.1080/03605300600783549. |
[9] |
N. Trudinger and X.-J. Wang, Hessian measures. I. Dedicated to Olga Ladyzhenskaya, Topo. Methods Nonlinear Anal., 10 (1997), 225-239. |
[10] |
N. Trudinger and X.-J. Wang, Hessian measures. II, Ann. of Math. (2), 150 (1999), 579-604.
doi: 10.2307/121089. |
[11] |
N. Trudinger and X.-J. Wang, Hessian measures. III, J. Funct. Anal., 193 (2002), 1-23.
doi: 10.1006/jfan.2001.3925. |
show all references
References:
[1] |
L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equations. III. Functions of the eigenvalues of the Hessian, Acta Math., 155 (1985), 261-301.
doi: 10.1007/BF02392544. |
[2] |
H. Fujita, On the blowing up of solutions of the Cauchy problems for $u_t=\Delta u + u^{1+\alpha}$, J. Fac. Sci. Univ. Tokyo, Sect. I, 13 (1966), 109-124. |
[3] |
K. Hayakawa, On the nonexistence of global solutions of some semilinear parabolic equations, Proc. Japan Acad., 49 (1973), 503-505.
doi: 10.3792/pja/1195519254. |
[4] |
D. Labutin, Potential estimates for a class of fully nonlinear elliptic equations, Duke Math. J., 111 (2002), 1-49.
doi: 10.1215/S0012-7094-02-11111-9. |
[5] |
E. Mitidieri and S. Pohozaev, Towards a unified approach to nonexistence of solutions for a class of differential inequalities, Milan J. Math., 72 (2004), 129-162.
doi: 10.1007/s00032-004-0032-7. |
[6] |
Q. Ou, Nonexistence results for Hessian inequality, Methods Appl. Anal., 17 (2010), 213-223.
doi: 10.4310/MAA.2010.v17.n2.a5. |
[7] |
N. C. Phuc and I. E. Verbitsky, Quasilinear and Hessian equations of Lane-Emden type, Ann. of Math., 168 (2008), 859-914.
doi: 10.4007/annals.2008.168.859. |
[8] |
N. C. Phuc and I. E. Verbitsky, Local integral estimates and removable singularities for quasilinear and Hessian equations with nonlinear source terms, Comm. Partial Differential Equations, 31 (2006), 1779-1791.
doi: 10.1080/03605300600783549. |
[9] |
N. Trudinger and X.-J. Wang, Hessian measures. I. Dedicated to Olga Ladyzhenskaya, Topo. Methods Nonlinear Anal., 10 (1997), 225-239. |
[10] |
N. Trudinger and X.-J. Wang, Hessian measures. II, Ann. of Math. (2), 150 (1999), 579-604.
doi: 10.2307/121089. |
[11] |
N. Trudinger and X.-J. Wang, Hessian measures. III, J. Funct. Anal., 193 (2002), 1-23.
doi: 10.1006/jfan.2001.3925. |
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