Some remarks on singular solutions of nonlinear elliptic equations. I

By Luis Caffarelli, Yanyan Li, L. Nirenberg. 2009

83 citations recorded by the source corpus.

Abstract.We study strong maximum principles for singular solutions of nonlinear elliptic and degenerate elliptic equations of second order. An application is given on symmetry of positive solutions in a punctured ball using the method of moving planes.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c5bbbcf2f4ec670066e842f2e49f02fa42b01382

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

A family of degenerate elliptic operators: Maximum principle and its consequences (2016, unknown): “More recently, in a PDE context, we wish to recall the works of Harvey and Lawson [18, 19] that have given a new geometric interpretation of solutions, while Caffarelli, Li and Nirenberg in [10, 11] in their study of degenerate elliptic equations, give some results concerning removable singularities”
Some Remarks on Singular Solutions of Nonlinear Elliptic Equations III: Viscosity Solutions Including Parabolic Operators (2011, background): “(1) (Note that in this paper F (x, u,∇u,∇2u) amounts to F (x, u,∇u,−∇2u) in [3] — a change of notation.)”
Fundamental solutions of homogeneous fully nonlinear elliptic equations (2009, background): “We also note that in the last several years there has been a great amount of interest of singular solutions of conformally invariant fully nonlinear equations (we refer to [19, 18, 5] and the references in these works).”