On higher order elliptic and parabolic inequalities with singularities on the boundary

被引：0
作者：
E. I. Galakhov
机构：
[1] Russian Academy of Sciences,Steklov Mathematical Institute
来源：
Proceedings of the Steklov Institute of Mathematics | 2010年 / 269卷
关键词：
STEKLOV Institute; Point Singularity; Steklov Inst; Quasilinear Elliptic Equation; Nonlinear Capacity;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We prove the nonexistence of solutions to a number of higher order quasilinear elliptic and parabolic partial differential inequalities in bounded domains with point singularities on the boundary. The results are extended to systems of such inequalities. The proofs are based on the method of nonlinear capacity. We also present examples showing that the conditions obtained are sharp in the class of problems under consideration.
引用
收藏
页码：76 / 84
页数：8
相关论文
共 22 条
[1]  
Galakhov E. I.(2008)On Differential Inequalities with Point Singularities on the Boundary Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 260 119-129
[2]  
Galakhov E. I.(2009)Elliptic and Parabolic Inequalities with Point Singularities on the Boundary Mat. Sb. 200 3-24
[3]  
Demyanov A. V.(2006)On Solvability of the Dirichlet Problem for the Semilinear Schrödinger Equation with Singular Potential Zap. Nauchn. Semin. POMI 336 25-45
[4]  
Nazarov A. I.(1998)The Absence of Global Positive Solutions to Quasilinear Elliptic Inequalities Dokl. Akad. Nauk 359 456-460
[5]  
Mitidieri E.(1999)Nonexistence of Positive Solutions for a System of Quasilinear Elliptic Equations and Inequalities in ℝ Dokl. Akad. Nauk 366 13-17
[6]  
Pokhozhaev S. I.(1999)Nonexistence of Positive Solutions for Quasilinear Elliptic Problems on ℝ Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 227 192-222
[7]  
Mitidieri E.(1997)The Essentially Nonlinear Capacities Induced by Differential Operators Dokl. Akad. Nauk 357 592-594
[8]  
Pohozaev S. I.(2003)Necessary Conditions for the Existence of Local Solutions to Higher-Order Singular Nonlinear Ordinary Differential Equations and Inequalities Dokl. Akad. Nauk 388 599-603
[9]  
Mitidieri E.(2002)On Necessary Conditions for the Existence of Local Solutions to Singular Nonlinear Ordinary Differential Equations and Inequalities Mat. Zametki 72 924-935
[10]  
Pohozaev S. I.(2001)Nonexistence Results and Estimates for Some Nonlinear Elliptic Problems J. Anal. Math. 84 1-49
123