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Schauder a priori estimates and regularity of solutions to degenerate-elliptic linear second-order partial differential equations
Paul Feehan and Camelia Pop
We establish Schauder a priori estimates and regularity for solutions to a class of degenerate-elliptic linear second-order partial differential equations. Furthermore, given a smooth source function, we prove regularity of solutions up to the portion of the boundary where the operator is degenerate. Degenerate-elliptic operators of the kind described in our article appear in a diverse range of applications, including as generators of affine diffusion processes employed in stochastic volatility models in mathematical finance, generators of diffusion processes arising in mathematical biology, and the study of porous media.