Regularity theory for fully nonlinear oblique transmission problems
Abstract
We develop a regularity theory for fully nonlinear oblique transmission problems. Our main result establishes optimal regularity of viscosity solutions for flat interfaces. For constant-coefficient equations, such solutions are found to be piecewise C1,α up to the interface. This regularity continues to hold for variable-coefficient equations with sufficiently regular coefficients in a more restrictive class of viscosity solutions.
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