Carleman Estimates, Optimal Three Cylinder Inequality, and Unique Continuation Properties for Solutions to Parabolic Equations

DOI10.1081/PDE-120020491zbMath1024.35021OpenAlexW2045435157MaRDI QIDQ4807602

Sergio Vessella

Publication date: 19 May 2003

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/pde-120020491

zbMATH Keywords

singular weight

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) A priori estimates in context of PDEs (35B45) Continuation and prolongation of solutions to PDEs (35B60) Second-order parabolic equations (35K10)

Related Items (14)

Quantitative uniqueness of solutions to parabolic equations ⋮ Quantitative uniqueness estimates for the generalized non-stationary Stokes system ⋮ Strong unique continuation for variable coefficient parabolic operators with Hardy type potential ⋮ Variable-coefficient parabolic theory as a high-dimensional limit of elliptic theory ⋮ Quantitative unique continuation for spectral subspaces of Schrödinger operators with singular potentials ⋮ Quantitative uniqueness for fractional heat type operators ⋮ Space-like quantitative uniqueness for parabolic operators ⋮ Matrix Li-Yau-Hamilton estimates under Ricci flow and parabolic frequency ⋮ Stability properties of an inverse parabolic problem with unknown boundaries ⋮ Approximate Two-Sphere One-Cylinder Inequality in Parabolic Periodic Homogenization ⋮ Carleman estimates for the parabolic transmission problem and Hölder propagation of smallness across an interface ⋮ A strong unique continuation property for the heat operator with Hardy type potential ⋮ Unique continuation for stochastic heat equations ⋮ Optimal three cylinder inequality at the boundary for solutions to parabolic equations and unique continuation properties

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• SOME PROPERTIES OF THE SOLUTIONS OF A LINEAR SECOND ORDER PARABOLIC EQUATION
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