Finite element approximation of unique continuation of functions with finite dimensional trace [PDF]
Mathematical Models and Methods in Applied Sciences, 2023 We consider a unique continuation problem where the Dirichlet trace of the solution is known to have finite dimension. We prove Lipschitz stability of the unique continuation problem and design a finite element method that exploits the finite ...
E. Burman, L. Oksanen
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Unique continuation for differential inclusions [PDF]
Annales de l'Institut Henri Poincare. Analyse non linéar, 2023 We consider the following question arising in the theory of differential inclusions: Given an elliptic set \Gamma and a Sobolev map u whose gradient lies in the quasiconformal envelope of \Gamma and touches \Gamma on a ...
Guido De Philippis +2 more
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Space-like strong unique continuation for some fractional parabolic equations [PDF]
Journal of Functional Analysis, 2022 In this paper we establish the space-like strong unique continuation for nonlocal equations of the type (∂t − ∆) u = V u, for 0 < s < 1. The proof of our main result, Theorem 1.1, is achieved via a conditional elliptic type doubling property for ...
Vedansh Arya +3 more
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Strong unique continuation and local asymptotics at the boundary for fractional elliptic equations [PDF]
Advances in Mathematics, 2021 . We study local asymptotics of solutions to fractional elliptic equations at boundary points, under some outer homogeneous Dirichlet boundary condition.
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A Gauge-Invariant Unique Continuation Criterion for Waves in Asymptotically Anti-de Sitter Spacetimes [PDF]
Communications in Mathematical Physics, 2022 We reconsider the unique continuation property for a general class of tensorial Klein–Gordon equations of the form □gϕ+σϕ=G(ϕ,∇ϕ),σ∈R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb ...
Athanasios Chatzikaleas, Arick Shao
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Failure of strong unique continuation for harmonic functions on RCD spaces [PDF]
Journal für die Reine und Angewandte Mathematik, 2022 Unique continuation of harmonic functions on RCD {\operatorname{RCD}} space is a long-standing open problem, with little known even in the setting of Alexandrov spaces.
Qintao Deng, Xinrui Zhao
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Quantitative unique continuation for the elasticity system with application to the kinematic inverse rupture problem [PDF]
Communications in Partial Differential Equations, 2022 We obtain explicit estimates on the stability of the unique continuation for a linear system of hyperbolic equations. In particular, our result applies to the elasticity system and also the Maxwell system.
Maarten V. de Hoop +3 more
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On Unique Continuation for Non-local Dispersive Models [PDF]
Vietnam Journal of Mathematics, 2021 We consider unique continuation properties of solutions to a family of evolution equations. Our interest is mainly on nonlinear non-local models.
F. Linares, G. Ponce
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Inverse source problem for a one-dimensional time-fractional diffusion equation and unique continuation for weak solutions [PDF]
Inverse Problems and Imaging, 2021 In this paper, we obtain the sharp uniqueness for an inverse \begin{document}$ x $\end{document}-source problem for a one-dimensional time-fractional diffusion equation with a zeroth-order term by the minimum possible lateral Cauchy data.
Zhi-yuan Li +2 more
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A Relative Entropy and a Unique Continuation Result for Ricci Expanders [PDF]
Communications on Pure and Applied Mathematics, 2021 We prove an optimal relative integral convergence rate for two expanding gradient Ricci solitons coming out of the same cone. As a consequence, we obtain a unique continuation result at infinity and prove that a relative entropy for two such self‐similar
Alix Deruelle, F. Schulze
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