共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper we establish a comparison result through symmetrization for solutions to some boundary value problems involving the fractional Laplacian. This allows to get sharp estimates for the solutions, obtained by comparing them with solutions of suitable radial problems. Furthermore, we use such result to prove a priori estimates for solutions in terms of the data, providing several regularity results which extend the well-known ones for the classical Laplacian. 相似文献
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V.G. Maz'ya 《Applicable analysis》2013,92(1-4):149-165
It is shown that the Wiener regularity of a boundary point with respect to the m-harmonic operator is a local property for the space dimensions n=2m,2m+1,2m+2 with m > 2 and n = 4,5,6,7 with m = 2. An estimate for the continuity modulus of the solution formulated in terms of the Wiener type m-capacitary integral is obtained for the same n and m. 相似文献
3.
For a one-phase free boundary problem involving a fractional Laplacian, we prove that “flat free boundaries” are C1,α. We recover the regularity results of Caffarelli for viscosity solutions of the classical Bernoulli-type free boundary problem with the standard Laplacian. 相似文献
4.
In this paper we localize some of Watanabe’s results on Wiener functionals of fractional regularity, and use them to give a precise estimate of the difference between two Donsker’s delta functionals even with fractional differentiability. As an application, the convergence rate of the density of the Euler scheme for non-Markovian stochastic differential equations is obtained. 相似文献
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In this article we are interested in interior regularity results for the solution \({\mu _ \in } \in C(\bar \Omega )\) of the Dirichlet problem where Ω is a bounded, open set and \({f_ \in } \in C(\bar \Omega )\) for all ? ∈ (0, 1). For some σ ∈ (0, 2) fixed, the operator \(\mathcal{I}_{\in}\) is explicitly given by which is an approximation of the well-known fractional Laplacian of order σ, as ? tends to zero. The purpose of this article is to understand how the interior regularity of u? evolves as ? approaches zero. We establish that u? has a modulus of continuity which depends on the modulus of f?, which becomes the expected Hölder profile for fractional problems, as ? → 0. This analysis includes the case when f? deteriorates its modulus of continuity as ? → 0.
相似文献
$$\{ _{\mu = 0in{\Omega ^c},}^{{I_ \in }(\mu ) = {f_ \in }in\Omega }$$
$${I_ \in }(\mu ,x) = \int_{{R^N}} {\frac{{[\mu (x + z) - \mu (x)]dz}}{{{ \in ^{N + \sigma }} + |z{|^{N + \sigma }}}}} ,$$
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8.
王兴 《纯粹数学与应用数学》2018,(1):42-51
因为奇异项使得分数阶Laplacian方程没有变分结构,所以临界点理论不能直接使用,成为研究此类方程弱解存在性的本质困难.本文首次运用闭锥上的临界点理论,得到奇异分数阶Laplacian方程的正弱解及其正则性.而且,此方法适用于其他奇异分数阶问题. 相似文献
9.
Jana Björn 《Calculus of Variations and Partial Differential Equations》2009,35(4):481-496
We use variational methods to obtain a pointwise estimate near a boundary point for quasisubminimizers of the p-energy integral and other integral functionals in doubling metric measure spaces admitting a p-Poincaré inequality. It implies a Wiener type condition necessary for boundary regularity for p-harmonic functions on metric spaces, as well as for (quasi)minimizers of various integral functionals and solutions of nonlinear
elliptic equations on R
n . 相似文献
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We study the regularity up to the boundary of solutions to the Dirichlet problem for the fractional Laplacian. We prove that if u is a solution of (−Δ)su=g in Ω , u≡0 in Rn\Ω, for some s∈(0,1) and g∈L∞(Ω), then u is Cs(Rn) and u/δs|Ω is Cα up to the boundary ∂Ω for some α∈(0,1), where δ(x)=dist(x,∂Ω). For this, we develop a fractional analog of the Krylov boundary Harnack method. 相似文献
13.
Positive solutions for multi‐point boundary value problems of fractional differential equations with p‐Laplacian 下载免费PDF全文
This paper investigates the existence of solutions for multi‐point boundary value problems of higher‐order nonlinear Caputo fractional differential equations with p‐Laplacian. Using the five functionals fixed‐point theorem, the existence of multiple positive solutions is proved. An example is also given to illustrate the effectiveness of ourmain result. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
14.
On large increments of a two-parameter fractional Wiener process 总被引:2,自引:0,他引:2
In this paper, how big the increments are and some liminf behaviors are studied of a two-parameter fractional Wiener process.
The results are based on some inequalities on the suprema of this process, which also are of independent interest 相似文献
15.
We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation
to study its obstacle problem. We write an equivalent characterization as a thin obstacle problem. In this way we are able
to apply local type arguments to obtain sharp regularity estimates for the solution and study the regularity of the free boundary. 相似文献
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V. A. Galaktionov 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(5):597-655
The classic problem of regularity of boundary points for higher-order partial differential equations (PDEs) is concerned.
For second-order elliptic and parabolic equations, this study was completed by Wiener’s (J. Math. Phys. Mass. Inst. Tech.
3:127–146, 1924) and Petrovskii’s (Math. Ann. 109:424–444, 1934) criteria, and was extended to more general equations including
quasilinear ones. Since the 1960–1970s, the main success was achieved for 2mth-order elliptic PDEs; e.g., by Kondrat’ev and Maz’ya. However, the higher-order parabolic ones, with infinitely oscillatory
kernels, were not studied in such details. As a basic model, explaining typical difficulties of regularity issues, the 1D
bi-harmonic equation in a domain shrinking to the origin (0, 0) is concentrated upon:
ut=-uxxxx in Q0 ={|x| < R(t), -1 < t < 0},u_t=-u_{xxxx}\,\,\, {\rm in}\, Q_0\,=\{|x| < R(t), \,\,-1 < t < 0\}, 相似文献
18.
Igor I. Skrypnik 《Mathematische Nachrichten》2011,284(16):2101-2122
We investigate the continuity of solutions for general nonlinear parabolic equations with non‐standard growth near a nonsmooth boundary of a cylindrical domain. We prove a sufficient condition for regularity of a boundary point. 相似文献
19.
Let be a weighted digraph with vertex set and arc set , where the arc weights are nonzero nonnegative symmetric matrices. In this paper, we obtain an upper bound on the signless Laplacian spectral radius of a weighted digraph , and if is strongly connected, we also characterize the digraphs achieving the upper bound. Moreover, we show that an upper bound of weighted digraphs or unweighted digraphs can be deduced from our upper bound. 相似文献
20.
Nasser-eddine Tatar 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(6):3209-3215
In this paper we consider the evolution of sound in a compressible fluid with reflection of sound at the surface of the material. The boundary controller involves a derivative of non-integer order. It is proved that solutions blow up in finite time in the presence of a nonlinear source. 相似文献
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