Boundary Unique Continuation on $$C^1$$-Dini Domains and the Size of the Singular Set
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DOI: 10.1007/s00205-022-01771-7
Abstract: Let $u$ be a harmonic function in a $C^1$-Dini domain $D$ such that $u$ vanishes on a boundary surface ball $\partial D \cap B_{5R}(0)$. We consider an effective version of its singular set (up to… read more here.
Keywords: set boundary; unique continuation; boundary unique; dini ... See more keywords
Strong unique continuation and local asymptotics at the boundary for fractional elliptic equations
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DOI: 10.1016/j.aim.2022.108279
Abstract: We study local asymptotics of solutions to fractional elliptic equations at boundary points, under some outer homogeneous Dirichlet boundary condition. Our analysis is based on a blow-up procedure which involves some Almgren type monotonicity formulæ… read more here.
Keywords: strong unique; elliptic equations; fractional elliptic; local asymptotics ... See more keywords
A unique continuation property for the wave equation in a time -dependent domain
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.125583
Abstract: Abstract We prove a unique continuation property for the wave eqiuation in a time-dependent domain Ω ( t ) , 0 ≤ t ≤ T . That is, if u ( t ) is a… read more here.
Keywords: unique continuation; continuation property; property wave; time dependent ... See more keywords
Unique continuation at the boundary for divergence form elliptic equations on quasiconvex domains
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DOI: 10.1063/5.0227056
Abstract: Let Ω⊂Rd be a quasiconvex Lipschitz domain, and let A(x) be a d × d uniformly elliptic, symmetric matrix with Lipschitz coefficients. Assume a nontrivial function u solves −∇ · (A(x)∇u) = 0 in Ω, and u… read more here.
Keywords: divergence form; form elliptic; unique continuation; boundary divergence ... See more keywords
Unique Continuation at Infinity: Carleman Estimates on General Warped Cylinders
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DOI: 10.1093/imrn/rnae147
Abstract: We obtain a vanishing result for solutions of the inequality $|\Delta u| \leq q_{1} |u| + q_{2} |\nabla u|$ that decay to zero along a very general warped cylindrical end of a Riemannian manifold. The… read more here.
Keywords: unique continuation; continuation infinity; general warped; infinity ... See more keywords
A Unique Continuation Property for the Level Set Equation
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DOI: 10.1093/imrn/rny148
Abstract: We prove the following unique continuation result: if a solution to the level set equation for mean curvature flow in a mean convex domain agrees to infinite order at the point where it attains its… read more here.
Keywords: set equation; unique continuation; level set;
New type of the unique continuation property for a fractional diffusion equation and an inverse source problem
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DOI: 10.1186/s13661-024-01827-5
Abstract: In this work, a new type of the unique continuation property for time-fractional diffusion equations is studied. The proof is mainly based on the Laplace transform and the properties of Bessel functions. As an application,… read more here.
Keywords: unique continuation; type unique; fractional diffusion; new type ... See more keywords
Symmetry analysis, persistence properties and unique continuation for the cross-coupled Camassa-Holm system
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DOI: 10.3934/dcds.2018016
Abstract: In this paper, we study symmetry analysis, persistence properties and unique continuation for the cross-coupled Camassa-Holm system. Lie symmetry analysis and similarity reductions are performed, some invariant solutions are also discussed. Then prove that the… read more here.
Keywords: unique continuation; symmetry analysis; system;
A unique continuation result for a system of nonlinear differential equations
Sign Up to like & getrecommendations! Published in 2023 at "Tamkang Journal of Mathematics"
DOI: 10.5556/j.tkjm.55.2024.5126
Abstract: Using an appropriate Carleman-type estimate, we establish a result of unique continuation for a special class of one-dimensional systems that model the evolution of long water waves with small amplitude in the presence of surface… read more here.
Keywords: continuation result; result system; system nonlinear; result ... See more keywords