Analysis of segregated boundary-domain integral equations for BVPs with non-smooth coefficients on Lipschitz domains [PDF]
Boundary Value Problems, 2017 Segregated direct boundary-domain integral equations (BDIEs) based on a parametrix and associated with the Dirichlet and Neumann boundary value problems for the linear stationary diffusion partial differential equation with a variable Hölder-continuous ...
S. Mikhailov
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Harmonic and Trace Inequalities in Lipschitz Domains [PDF]
, 2019 This is a preprint of a paper accepted 15-Nov-2018 and whose final and definite form is a book chapter at Springer New York, on the topic of 'Frontiers in Functional Equations and Analytic Inequalities', Edited by G.
Touhami, Soumia +2 more
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Planning With Learned Dynamics: Probabilistic Guarantees on Safety and Reachability via Lipschitz Constants [PDF]
IEEE Robotics and Automation Letters, 2020 We present a method for feedback motion planning of systems with unknown dynamics which provides probabilistic guarantees on safety, reachability, and goal stability.
Craig Knuth +3 more
semanticscholar +1 more source
Tangent Lines and Lipschitz Differentiability Spaces
Analysis and Geometry in Metric Spaces, 2016 We study the existence of tangent lines, i.e. subsets of the tangent space isometric to the real line, in tangent spaces of metric spaces.We first revisit the almost everywhere metric differentiability of Lipschitz continuous curves.
Cavalletti Fabio, Rajala Tapio
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The Inhomogeneous Dirichlet Problem in Lipschitz Domains
Journal of Functional Analysis, 1995 The inhomogeneous Dirichlet problem \[ \Delta u= f\qquad\text{on}\quad \Omega,\qquad u= 0\qquad\text{on}\quad \partial\Omega, \] with data in Sobolev spaces of domains \(\Omega\) in \(\mathbb{R}^n\) with Lipschitz boundary, is studied. There are certain special difficulties in this kind of domains, e.g.
Jerison, D., Kenig, C.E.
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Boundedness of the gradient of a solution to the Neumann-Laplace problem in a convex domain [PDF]
, 2008 It is shown that solutions of the Neumann problem for the Poisson equation in an arbitrary convex $n$-dimensional domain are uniformly Lipschitz. Applications of this result to some aspects of regularity of solutions to the Neumann problem on convex ...
Maz'ya, Vladimir
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The poisson problem on Lipschitz domains [PDF]
, 2021 The aim of this work is to describe the sharp ranges of indices, for which the Poisson problem for Laplacian with Dirichlet or Neumann boundary conditions is well-posed on the scales of Besov and Triebel-Lizorkin spaces on arbitrary Lipschitz domains. The main theorems we prove extend the work of D. Jerison and C.
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Resolvent Estimates in L^p for the Stokes Operator in Lipschitz Domains
, 2012 We establish the $L^p$ resolvent estimates for the Stokes operator in Lipschitz domains in $R^d$, $d\ge 3$ for $|\frac{1}{p}-1/2|< \frac{1}{2d} +\epsilon$.
B. Dahlberg +26 more
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The 𝐿^{𝑝} regularity problem on Lipschitz domains [PDF]
Transactions of the American Mathematical Society, 2010 This paper contains two results on the L p L^p
Kilty, Joel, Shen, Zhongwei
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General p-curl systems and duality mappings on Sobolev spaces for Maxwell equations
Electronic Journal of Differential Equations, 2020 We study a general p-curl system arising from a model of type-II superconductors. We show several trace theorems that hold on either a Lipschitz domain with small Lipschitz constant or on a C^{1,1} domain.
Dhruba R. Adhikari, Eric Stachura
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