Optimal boundary C^{1,α} regularity is proved for viscosity solutions to degenerate fully nonlinear equations with oblique boundary conditions and Hamiltonian terms.
Optimal $C^{1,\alpha}$ regularity up to the boundary for fully nonlinear elliptic equations with double phase degeneracy
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abstract
In this paper we establish optimal $C^{1,\alpha}$ regularity up to the boundary for viscosity solutions of fully nonlinear elliptic equations with double phase degeneracy law and oblique boundary conditions. The approach developed here relies on first deriving uniform boundary H\"older estimates for perturbed models with oblique boundary data in ``almost $C^{1}$-flat'' domains. Building upon these estimates, the desired regularity is obtained through a compactness and stability framework for viscosity solutions. As a byproduct of our analysis, we determine the optimal H\"older exponent for solutions when the governing operator is quasiconvex or quasiconcave. In addition, we establish an improved regularity result along vanishing points of the source term.
fields
math.AP 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Global C^{1,α} regularity is established for viscosity solutions of singular/degenerate fully nonlinear elliptic equations with oblique boundary conditions, extending previous work to the singular case.
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Sharp regularity for degenerate fully nonlinear equations with oblique boundary conditions and Hamiltonian terms
Optimal boundary C^{1,α} regularity is proved for viscosity solutions to degenerate fully nonlinear equations with oblique boundary conditions and Hamiltonian terms.
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C^{1,\alpha} regularity for a class of singular/degenerate fully nonlinear elliptic equations with oblique boundary conditions
Global C^{1,α} regularity is established for viscosity solutions of singular/degenerate fully nonlinear elliptic equations with oblique boundary conditions, extending previous work to the singular case.