Riesz capacity, maximum principle and removable sets of fully nonlinear second order elliptic operators. (English) Zbl 1299.35120

Amendola, M. E.; Galise, G.; Vitolo, A.

Differ. Integral Equ. 26, No. 7-8, 845-866 (2013).

The authors study the second-order uniformly elliptic operators \(F=F(Du,D^2u)\) that are Lipschitz continuous in the gradient variable. They show sufficient conditions for the extended maximum principle and the removable singularities for viscosity solutions of \(F\) via Riesz and logarithmic capacity.

Reviewer: Lubomira Softova (Aversa)

MSC:

35J60	Nonlinear elliptic equations
35B50	Maximum principles in context of PDEs
35B51	Comparison principles in context of PDEs
35B60	Continuation and prolongation of solutions to PDEs

Keywords:

maximum principle; nonlinear elliptic operator; viscosity solution; Riesz capacity