Hölder estimates and asymptotic behaviors of solutions of some degenerate elliptic equations on half-spaces

2021/08/28 by Xiaobiao Jia, Jia, Xiaobiao
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2108.12646

openalex publication_date 2021/08/28 · openalex created_date 2021/09/13 · openalex updated_date 2026/07/28

Abstract

In this paper we report the asymptotic behaviors of viscosity solutions of the following degenerate elliptic equations Lu=x_n^2α∑_i,j=1^n-1a_ij(x)D_iju(x) +2x_n^α∑_i=1^n-1a_in(x)D_inu(x)+D_nnu(x)=0 outside a bounded domain of the upper half space for α>0 with proper coefficients. Meanwhile, the Hölder estimates up to the boundary will be obtained using rescaling methods.

Citations

• Analysis of degenerate elliptic operators of Grušin type

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