Dirichlet对Neumann算子的强制性及其在Muscat问题中的应用

IF 0.3 Q4 MATHEMATICS

Acta Mathematica Vietnamica Pub Date : 2022-11-03 DOI:10.1007/s40306-022-00484-z

Huy Q. Nguyen

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引用次数: 1

摘要

我们考虑带Lipschitz边界的带状和半空间域中的Dirichlet到Neumann算子。证明了Dirichlet到Neumann算子生成的二次型控制了一些尖锐的齐次分式Sobolev范数。作为一个应用，我们证明了Dong等人（2021）构造的单相Muscat问题的全局Lipschitz解在任何Hölder范数Cα，α∈（0,1）中随时间呈指数衰减。

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

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 Hölder norm C^α, α ∈ (0,1).

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来源期刊

Acta Mathematica Vietnamica MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

期刊介绍： Acta Mathematica Vietnamica is a peer-reviewed mathematical journal. The journal publishes original papers of high quality in all branches of Mathematics with strong focus on Algebraic Geometry and Commutative Algebra, Algebraic Topology, Complex Analysis, Dynamical Systems, Optimization and Partial Differential Equations.