2023/10/28 by Lu Chen, Chen, Lu, Rou Jiang +3
Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Heterotopic Ossification and Related Conditions #Muscle and Compartmental Disorders #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2310.18848
openalex publication_date 2023/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let F be convex and homogeneous of degree 1, its polar Fo represent a finsler metric on ℝn, and Ω be any bounded open set in ℝn. In this paper, we first construct the theoretical structure of anisotropic harmonic transplantation. Using the anisotropic harmonic transplantation, co-area formula, limiting Sobolev approximation method, delicate estimate of level set of Green function, we investigate the optimal concentration level of the Trudinger-Moser functional ∫Ωe^λn|u|(n)/(n-1)dx under the anisotropic Dirichlet norm constraint ∫ΩFn( ∇u) dx≤1, where λn=n(n)/(n-1)κn(1)/(n-1) denotes the sharp constant of anisotropic Trudinger-Moser inequality in bounded domain and κn is the Lebesgue measure of the unit Wulff ball. As an application. we can immediately deduce the existence of extremals for anisotropic Trudinger-Moser inequality on bounded domain. Finally, we also consider the optimal concentration level of the anisotropic singular Trudinger-Moser functional. The method is based on the limiting Hardy-Sobolev approximation method and constructing a suitable normalized anisotropic concentrating sequence.