On a new Kato class and positive solutions of Dirichlet problems for the fractional Laplacian in bounded domains

Chemmam R.; Magli H.; Masmoudi S.

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On a new Kato class and positive solutions of Dirichlet problems for the fractional Laplacian in bounded domains

机译：关于一类新的加藤类和有界域分数拉普拉斯算子Dirichlet问题的正解

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The purpose of this paper is to extend some results of the potential theory of an elliptic operator to the fractional Laplacian (-Δ)α2, 0<α<2, in a bounded C1,1 domain D in Rn. In particular, we introduce a new Kato class Kα(D) and we exploit the properties of this class to study the existence of positive solutions of some Dirichlet problems for the fractional Laplacian.

机译：本文的目的是将椭圆算子的势能理论的某些结果扩展到Rn中有界C1,1域D中的分数拉普拉斯（-Δ）α2，0 <α<2。特别是，我们引入了一个新的Kato类Kα（D），并且利用此类的性质来研究分数拉普拉斯算子的某些Dirichlet问题正解的存在性。

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来源
《Nonlinear Analysis: An International Multidisciplinary Journal》 |2011年第5期|共22页
作者
Chemmam R.; Magli H.; Masmoudi S.;
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正文语种 eng
中图分类数学分析;
关键词
Dirichlet problem; Fractional Laplacian; Green function; Harmonic function; Martin boundary; Martin representation; Symmetric stable process;

机译：Dirichlet问题;分数拉普拉斯算子;格林函数;调和函数;马丁边界;马丁表示;对称稳定过程;

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1. On a new Kato class and positive solutions of Dirichlet problems for the fractional Laplacian in bounded domains [J] . Chemmam R., Magli H., Masmoudi S. Nonlinear Analysis: An International Multidisciplinary Journal . 2011,第5期

机译：关于一类新的加藤类和有界域分数拉普拉斯算子Dirichlet问题的正解
2. Existence and Uniqueness of Positive Solution for a Fractional Dirichlet Problem with Combined Nonlinear Effects in Bounded Domains [J] . ImedBachar, HabibMaagli Abstract and applied analysis . 2013,第10期

机译：有界域上具有非线性效应的分数阶Dirichlet问题正解的存在性和唯一性
3. On a new Kato class and singular solutions of a nonlinear elliptic equation in bounded domains of R-n [J] . Maagli H, Zribi M Positivity . 2005,第4期

机译：关于R-n有界域中的非线性椭圆方程的新的Kato类和奇异解
4. Speptral Fractional Laplacian with Inhomogeneous Dirichlet Data: Questions, Problems, Solutions [C] . S. Harizanov, S. Margenov, N. Popivanov Annual Meeting of the Bulgarian Section of SIAM . 2018

机译：具有非依然Dirichlet数据的刺刀分数Laplacian：问题，问题，解决方案
5. Normalized p-laplacian evolution: boundary behavior of non-negative solutions of fully nonlinear parabolic equations: Gradient bounds for p-harmonic systems with vanishing neumann (dirichlet) data in a convex domain. [D] . Banerjee, Agnid. 2014

机译：归一化的p-拉普拉斯演化：完全非线性抛物方程的非负解的边界行为：具有在凸域中消失的Neumann（dirichlet）数据的p调和系统的梯度界。
6. Multiple Solutions for a Class of Dirichlet Double Eigenvalue Quasilinear Elliptic Systems Involving the (p1… pn)-Laplacian Operator [O] . Armin Hadjian, Saleh Shakeri 2013

机译：一类Dirichlet双特征值拟线性椭圆系统的多重解其中（p1…pn）-拉普拉斯算子
7. Existence and Uniqueness of Positive Solution for a Fractional Dirichlet Problem with Combined Nonlinear Effects in Bounded Domains [O] . Imed Bachar, Habib Mâagli 2013

机译：界域中的非线性效应分数Dirichlet问题的阳性解的存在性和唯一性
8. The Solution of the Dirichlet Problem for Lapalce's Equation when the Boundary Data is Discontinuous and the Domain has a Boundary which is of Bounded Rotation by Means of the Lebesgue-Stieltjes Integral Equation for the Double Layer Potential [R] . Cryer, C. W. 1970

机译：利用Lebesgue-stieltjes积分方程对双层势进行边界数据不连续且域具有有界旋转边界的Dirichlet问题的解

On a new Kato class and positive solutions of Dirichlet problems for the fractional Laplacian in bounded domains

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