Monotonicity of generalized frequencies and the strong unique continuation property for fractional parabolic equations

DOI10.1016/j.aim.2018.07.021zbMath1400.35045arXiv1709.07243OpenAlexW2964166239WikidataQ129440438 ScholiaQ129440438MaRDI QIDQ1790253

Agnid Banerjee, Nicola Garofalo

Publication date: 2 October 2018

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.07243

zbMATH Keywords

fractional heat equationmonotonicity of the frequency

Mathematics Subject Classification ID

Continuation and prolongation of solutions to PDEs (35B60) Second-order parabolic equations (35K10) Fractional partial differential equations (35R11)

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Cites Work

• Unnamed Item
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• Extension properties and boundary estimates for a fractional heat operator
• A Harnack inequality for fractional Laplace equations with lower order terms
• Fractional powers of closed operators and the semigroups generated by them
• A remark on a Harnack inequality for dengerate parabolic equations
• A fundamental solution for the heat equation which is supported in a strip
• Unique continuation for parabolic operators
• Unique continuation for fractional orders of elliptic equations
• On the regularity of the non-dynamic parabolic fractional obstacle problem
• Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
• On a fractional Nirenberg problem. I: Blow up analysis and compactness of solutions
• Local behavior of solutions of quasilinear parabolic equations
• L'intégrale de Riemann-Liouville et le problème de Cauchy
• Unique continuation for elliptic operators: A geometric-variational approach
• The local regularity of solutions of degenerate elliptic equations
• On the behavior of the solutions of degenerate parabolic equations
• Characterization of traces of the weighted Sobolev space $W^{1,p}(\Omega,d_M^\epsilon)$ on $M$
• Qnique Continuation for
• Doubling properties of caloric functions
• Unique Continuation for Fractional Schrödinger Equations with Rough Potentials
• Optimal Regularity and the Free Boundaryin the Parabolic Signorini Problem
• Regularity Theory and Extension Problem for Fractional Nonlocal Parabolic Equations and the Master Equation
• Unique Continuation Property and Local Asymptotics of Solutions to Fractional Elliptic Equations
• An Extension Problem Related to the Fractional Laplacian
• A harnack inequality for parabolic differential equations
• On a pointwise estimate for parabolic differential equations
• Backward uniqueness for parabolic operators with variable coefficients in a half space