Symmetry of large solutions of nonlinear elliptic equations in a ball

Let g be a locally Lipschitz continuous real-valued function which satisfies the Keller–Osserman condition and is convex at infinity, then any large solution of −Δu+g(u)=0 in a ball is radially symmetric.

[1]  Laurent Veron,et al.  Semilinear elliptic equations with uniform blow-up on the boundary , 1992 .

[2]  Yihong Du,et al.  Boundary blow-up solutions with a spike layer , 2004 .

[3]  Laurent Véron,et al.  Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations , 1997 .

[4]  Yihong Du,et al.  Uniqueness and layer analysis for boundary blow-up solutions , 2004 .

[5]  R. Letelier,et al.  Multiple boundary blow-up solutions for nonlinear elliptic equations , 2003, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[6]  C. Bandle,et al.  Asymptotic behaviour of solutions and their derivatives, for semilinear elliptic problems with blowup on the boundary , 1995 .

[7]  J. Keller On solutions of δu=f(u) , 1957 .

[8]  L. Nirenberg,et al.  Partial Differential Equations Invariant under Conformal or Projective Transformations , 1974 .

[9]  Yihong Du,et al.  Boundary blow-up solutions and their applications in quasilinear elliptic equations , 2003 .

[10]  W. Walter,et al.  Symmetry and multiplicity for nonlinear elliptic differential equations with boundary blow-up , 1997 .

[11]  James Serrin,et al.  A symmetry problem in potential theory , 1971 .

[12]  L. Véron,et al.  Asymptotic behaviour for the gradient of large solutions to some nonlinear elliptic equations , 2008, 0805.2533.

[13]  Robert Osserman,et al.  On the inequality $\Delta u\geq f(u)$. , 1957 .

[14]  R. Redheffer On the inequality Δu⩾f(u,¦grad u¦) , 1960 .

[15]  J. Matero Quasilinear elliptic problems with boundary blow-up , 1995 .

[16]  Lipman Bers,et al.  Contributions to analysis : a collection of papers dedicated to Lipman Bers , 1974 .

[17]  Porretta Alessio,et al.  Asymptotic Behaviour of the Gradient of Large Solutions to Some Nonlinear Elliptic Equations , 2006 .

[18]  B. Gidas,et al.  Symmetry and related properties via the maximum principle , 1979 .