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arXiv · 2303.01190

Regularity of solutions to degenerate normalized $p$-Laplacian equation with general variable exponents

Jiangwen Wang·Yunwen Yin·Feida Jiang
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Abstract

In this paper, we consider a kind of degenerate normalized $p$-Laplacian equation with general variable exponents. We establish local $C^{1,\alpha'}$ regularity of viscosity solutions by making use of the compactness argument, scaling techniques and the localized oscillating method. In addition, we also obtain almost optimal pointwise $C^{1,\tau} $ regularity for degenerate free transmission problem related to normalized $ p$-Laplacian. Our argument is based on a new improved oscillation-type estimate combined with a localized analysis.

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Jiangwen Wang, Yunwen Yin, Feida Jiang. 2023-03-02. Regularity of solutions to degenerate normalized $p$-Laplacian equation with general variable exponents. https://doi.org/10.1007/s11118-025-10228-x

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