On a class of nonlocal obstacle type problems related to the distributional Riesz fractional derivative

IF 0.5 4区数学 Q3 MATHEMATICS

Portugaliae Mathematica Pub Date : 2021-01-18 DOI:10.4171/PM/2100

Catharine Lo, J. Rodrigues

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引用次数: 3

Abstract

In this work, we consider the nonlocal obstacle problem with a given obstacle $\psi$ in a bounded Lipschitz domain $\Omega$ in $\mathbb{R}^{d}$, such that $\mathbb{K}_\psi^s=\{v\in H^s_0(\Omega):v\geq\psi \text{ a.e. in }\Omega\}\neq\emptyset$, given by \[u\in\mathbb{K}_\psi^s:\langle\mathcal{L}_au,v-u\rangle\geq\langle F,v-u\rangle\quad\forall v\in\mathbb{K}^s_\psi,\] for $F\in H^{-s}(\Omega)$, the dual space of $H^s_0(\Omega)$, $0

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一类与分布Riesz分数阶导数有关的非局部障碍型问题

在这项工作中，我们考虑了在$\mathbb｛R｝^｛d｝$中有界Lipschitz域$\Omega$中给定障碍物$\psi$的非局部障碍问题，使得$\mathbb{K}_\psi^s=\{v\in H^s_0（\Omega）：v\geq\psi\text｛a.e.in｝\Omega\｝\neq\pemptyset$，由\[u\in\mathbb给出{K}_\psi ^s:\langle\mathcal{L}_au，v-u\rangle\geq\langle F，v-u\ rangle\quad\ for all v\in\mathbb｛K｝^s_\psi，\]对于$F\in H^｛-s｝（\Omega）$，$H^s_0（\Ome茄）$的对偶空间，$0

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来源期刊

Portugaliae Mathematica MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： Since its foundation in 1937, Portugaliae Mathematica has aimed at publishing high-level research articles in all branches of mathematics. With great efforts by its founders, the journal was able to publish articles by some of the best mathematicians of the time. In 2001 a New Series of Portugaliae Mathematica was started, reaffirming the purpose of maintaining a high-level research journal in mathematics with a wide range scope.

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