Coercivity of the Dirichlet-to-Neumann Operator and Applications to the Muskat Problem

被引：0

作者：

Nguyen, Huy Q. ^{[1
]}

机构：

[1] Univ Maryland, Dept Math, College Pk, MD 20742 USA

来源：

ACTA MATHEMATICA VIETNAMICA | 2023年 / 48卷 / 01期

关键词：

Dirichlet-to-Neumann operator; Coercivity; Muskat problem; Time decay of solutions;

D O I：

10.1007/s40306-022-00484-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the Dirichlet-to-Neumann operator in strip-like and half-space domains with Lipschitz boundary. It is shown that the quadratic form generated by the Dirichlet-to-Neumann operator controls some sharp homogeneous fractional Sobolev norms. As an application, we prove that the global Lipschitz solutions constructed in Dong et al. (2021) for the one-phase Muskat problem decays exponentially in time in any Holder norm C-alpha, alpha is an element of (0,1).

引用

页码：51 / 62

页数：12

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