Removable singularities of solutions to a class of quasilinear non- uniformly elliptic equations. (English) Zbl 0655.35020
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.
Reviewer: C.F.Wang
MSC:
| 35J60 | Nonlinear elliptic equations |
| 35J67 | Boundary values of solutions to elliptic equations and elliptic systems |
| 35B65 | Smoothness and regularity of solutions to PDEs |
Keywords:
quasilinearReferences:
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