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arXiv · 2103.12938

Regularity of solutions to degenerate fully nonlinear elliptic equations with variable exponent

Yuzhou Fang·Vicentiu D. Radulescu·Chao Zhang
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Abstract

We consider the fully nonlinear equation with variable-exponent double phase type degeneracies $$ \big[|Du|^{p(x)}+a(x)|Du|^{q(x)}\big]F(D^2u)=f(x). $$ Under some appropriate assumptions, by making use of geometric tangential methods and combing a refined improvement-of-flatness approach with compactness and scaling techniques we obtain the sharp local $C^{1,\alpha}$ regularity of viscosity solutions to such equations.

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Yuzhou Fang, Vicentiu D. Radulescu, Chao Zhang. 2021-03-24. Regularity of solutions to degenerate fully nonlinear elliptic equations with variable exponent. https://arxiv.org/abs/2103.12938

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