Removable singularities of solutions to a class of quasilinear non- uniformly elliptic equations
Let \(\Omega\) be a bounded domain of \({\mathbb{R}}^ n,\) \(n\geq 2\), and K be a compact subset of \(\Omega\). Suppose \(u\in C^ 2(\Omega/k)\) satisfies the quasilinear equations: \[ (1)\quad div A(x,Du)=B(x,u). \] Here \(A=(A_ 1,...,A_ n)\) is a given vector-valued function of \((x,p)\in \Omega \times {\mathbb{R}}^ n\) and B is a given scalar function. Under some conditions on A, B and K, the author proves that u can be defined on K so that the resulting function is a C 2 solution of (1) in all of \(\Omega\). In which the singular set K can indeed be allowed to approach the boundary and some interesting examples are given.
scientific article; zbMATH DE number 4069409
scientific article