On fractional parabolic equations with Hardy-type potentials
Veronica Felli, Ana Primo, Giovanni Siclari
TL;DR
This paper studies fractional heat equations with Hardy-type potentials, classifying their local behaviors and proving strong unique continuation properties using advanced monotonicity formulas and blow-up analysis.
Contribution
It introduces a new classification framework for local profiles and establishes strong unique continuation for fractional parabolic equations with Hardy potentials.
Findings
Classification of local asymptotic profiles
Proof of strong unique continuation properties
Development of an Almgren-Poon monotonicity formula
Abstract
A classification of local asymptotic profiles and strong unique continuation properties are established for a class of fractional heat equations with a Hardy-type potential, via an Almgren-Poon monotonicity formula combined with a blow-up analysis.
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Taxonomy
TopicsFractional Differential Equations Solutions · Nonlinear Partial Differential Equations · Numerical methods in inverse problems