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This is a Quantitative Study study.

October 20, 2025Open Access

Harnack inequality for a class of degenerate fully nonlinear pseudo-p-Laplacian equations

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Harnack inequalities are established for viscosity solutions, improving understanding of solution behaviors.
Interior Hölder regularity is proved, showcasing the smoothness of solutions in the presence of degeneracy.
The approach utilizes a modified sliding paraboloid method with anisotropic functions tailored to the degeneracy.
This work extends techniques in nonlinear differential equations, highlighting connections to other mathematical areas.

Implication

Proving Hölder regularity and Harnack inequalities for viscosity solutions in degenerate equations, indicating potential for broader applications.

Abstract

We prove interior Hölder regularity and Harnack inequalities for viscosity solutions of a class of degenerate fully nonlinear pseudo-p-Laplacian equations in nondivergence form. Our main approach is an adaptation of the sliding paraboloid method with anisotropic functions tailored to the coordinatewise degeneracy.

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Cite This Study

Byun et al. (2025) studied this question.

synapsesocial.com/papers/68f5fcce8d54a28a75cf1c08 https://doi.org/10.48550/arxiv.2509.24442

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Implication

Proving Hölder regularity and Harnack inequalities for viscosity solutions in degenerate equations, indicating potential for broader applications.

Harnack inequality for a class of degenerate fully nonlinear pseudo-p-Laplacian equations

Key Points

Implication

Abstract

Discussion

Cite This Study

Harnack inequality for a class of degenerate fully nonlinear pseudo-p-Laplacian equations

Key Points

Implication

Abstract

Discussion

Cite This Study

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