共查询到20条相似文献,搜索用时 10 毫秒
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Potential Analysis - We prove a boundary Harnack inequality for nonlocal elliptic operators L in non-divergence form with bounded measurable coefficients. Namely, our main result establishes that... 相似文献
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On a bounded C
2-domain
we consider the singular boundary-value problem 1/2u=f(u) in D, u
D
=, where d3, f:(0,)(0,) is a locally Hölder continuous function such that f(u) as u0 at the rate u
–, for some (0,1), and is a non-negative continuous function satisfying certain growth assumptions. We show existence of solutions bounded below by a positive harmonic function, which are smooth in D and continuous in
. Such solutions are shown to satisfy a boundary Harnack principle. 相似文献
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In this paper we study the Martin boundary of unbounded open sets at infinity for a large class of subordinate Brownian motions. We first prove that, for such subordinate Brownian motions, the uniform boundary Harnack principle at infinity holds for arbitrary unbounded open sets. Then we introduce the notion of κ-fatness at infinity for open sets and show that the Martin boundary at infinity of any such open set consists of exactly one point and that point is a minimal Martin boundary point. 相似文献
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In this paper we prove a uniform and scale invariant boundary Harnack principle at infinity for a large class of purely discontinuous Feller processes in metric measurespaces. 相似文献
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0 Introduction Because of applications to control theory, see Schmit and Week's work in [1], the following unique continuation question (UCP) was raised in [2-3]: if u is a harmonic function in a connected Lipschitz domainΩ, vanishing continuously on an open subsetΓof the boundary (?)Ωand whose normal derivative vanishes on a subset of Γof positive surface measure, does it follows that u is identically zero inΩ? On the other hand, the unique continuation problem has been focusing on second order equations in which the coefficients of the lower-order terms are allowed to be 相似文献
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Davide Guidetti 《Mathematische Nachrichten》2002,237(1):62-88
We prove a priori estimates in Sobolev spaces for general linear elliptic boundary value problems with VMO coefficients.We give also results of existence and uniqueness of a solution. 相似文献
10.
Let u be the solutions to some elliptic equations of the form
in some Lipschitz domains, a direct and elementary proof of the doubling property for u2 over balls near the boundary is presented, and the unique continuation at the boundary for Dini domains is founded.AMS Subject Classification (1991): 42B20, 35J10 相似文献
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This paper is concerned with the study of the diffusion process associated with a nondivergence form elliptic operator in d dimensions, d2. The authors introduce a new technique for studying the diffusion, based on the observation that the probability of escape from a d–1 dimensional hyperplane can be explicitly calculated. They use the method to estimate the probability of escape from d–1 dimensional manifolds which are C
1,
, and also d–1 dimensional Lipschitz manifolds. To implement their method the authors study various random walks induced by the diffusion process, and compare them to the corresponding walks induced by Brownian motion. 相似文献
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Andrzej Stós 《Bulletin des Sciences Mathématiques》2006,130(7):580
We prove the Boundary Harnack Principle related to fractional powers of Laplacian for some natural regions in the two-dimensional Sierpiński carpet. This is a natural application of some more general approach based on the Ikeda-Watanabe formula, that expresses the harmonic measure in terms the Green function of a given region and the Lévy measure of the semigroup. 相似文献
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Ruo Li & Fanyi Yang 《高等学校计算数学学报(英文版)》2021,14(4):1042-1067
We develop a new least squares method for solving the second-order elliptic equations in non-divergence form. Two least-squares-type functionals are proposed for solving the equation in two sequential steps. We first obtain a numerical
approximation to the gradient in a piecewise irrotational polynomial space. Then
together with the numerical gradient, we seek a numerical solution of the primitive
variable in the continuous Lagrange finite element space. The variational setting
naturally provides an a posteriori error which can be used in an adaptive refinement
algorithm. The error estimates under the $L^2$ norm and the energy norm for both
two unknowns are derived. By a series of numerical experiments, we verify the
convergence rates and show the efficiency of the adaptive algorithm. 相似文献
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利用Banach空间锥理论、算子的指数理论、上下解理论研究了含有一致椭圆型算子的椭圆边值问题变号解的存在性,同时分别得到了一个正解和一个负解.特别当非线性项是奇函数时,该边值问题至少存在一个正解,一个负解和两个变号解. 相似文献
18.
We establish a boundary Harnack principle for a large class of subordinate Brownian motions, including mixtures of symmetric stable processes, in κ-fat open sets (disconnected analogue of John domains). As an application of the boundary Harnack principle, we identify the Martin boundary and the minimal Martin boundary of bounded κ-fat open sets with respect to these processes with their Euclidean boundaries. 相似文献
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Boundary Value Problems for Second‐Order Elliptic Operators Satisfying a Carleson Condition 下载免费PDF全文
Let Ω be a Lipschitz domain in , and be a second‐order elliptic operator in divergence form. We establish the solvability of the Dirichlet regularity problem with boundary data in and of the Neumann problem with data for the operator L on Lipschitz domains with small Lipschitz constant. We allow the coefficients of the operator L to be rough, obeying a certain Carleson condition with small norm. These results complete the results of Dindo?, Petermichl, and Pipher (2007), where the Dirichlet problem was considered under the same assumptions, and Dindo? and Rule (2010), where the regularity and Neumann problems were considered on two‐dimensional domains.© 2016 Wiley Periodicals, Inc. 相似文献
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Potential Analysis - In this article we establish the exact growth of the solution to the singular quasilinear p-parabolic free boundary problem in non-divergence form near the free boundary from... 相似文献