非线性锥退化 Laplace 方程的比较原理——献给陈化教授70寿辰

Abstract

Abstract:

This paper concerns a class of non-divergence non-linear elliptic equations driven by the cone degenerate Laplacian motivated by cone calculus, as follows $$t^{-2}{\rm div}_ \mathbb{B}(\nabla_ \mathbb{B}u) +t^{-2}(n-2)(t\partial_t u)+h(u)=f(t,x) \ \ \ \ (t,x) \in \mathbb{B}.$$ Using a special auxiliary function, we establish the comparison principle for the viscosity solutions under some assumptions on $f$ and $h$, and then obtain the uniqueness of the viscosity solutions for the corresponding Dirichlet problem.

Key words: comparison principle, conical singularity, degenerate elliptic equations

CLC Number:

O175.25

Yawei Wei, Mengnan Zhang. Comparison Principle for Nonlinear Cone Degenerate Laplace Equations[J].Acta mathematica scientia,Series A, 2026, 46(2): 503-517.

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References 26

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Comparison Principle for Nonlinear Cone Degenerate Laplace Equations

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