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

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.

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
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