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arXiv · 1812.11428

Regularity of solutions to a class of variable-exponent fully nonlinear elliptic equations

Anne C. Bronzi·Edgard A. Pimentel·Giane C. Rampasso·Eduardo V. Teixeira
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Abstract

In the present paper, we propose the investigation of variable-exponent, degenerate/singular elliptic equations in non-divergence form. This current endeavor parallels the by now well established theory of functionals satisfying nonstandard growth condition, which in particular encompasses problems ruled by the $p(x)$-laplacian operator. Under rather general conditions, we prove viscosity solutions to variable exponent fully nonlinear elliptic equations are locally of class $C^{1,\kappa}$ for a universal constant $0< \kappa < 1$. A key feature of our estimates is that they do not depend on the modulus of continuity of exponent coefficients, and thus may be employed to investigate a variety of problems whose ellipticity degenerates and/or blows-up in a discontinuous fashion.

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Anne C. Bronzi, Edgard A. Pimentel, Giane C. Rampasso, Eduardo V. Teixeira. 2018-12-29. Regularity of solutions to a class of variable-exponent fully nonlinear elliptic equations. https://arxiv.org/abs/1812.11428

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