Unique continuation from the edge of a crack

Autor:	De Luca, Alessandra, Felli, Veronica
Rok vydání:	2020
Předmět:	Mathematics - Analysis of PDEs 35J15 35C20 74A45
Druh dokumentu:	Working Paper
Popis:	In this work we develop an Almgren type monotonicity formula for a class of elliptic equations in a domain with a crack, in the presence of potentials satisfying either a negligibility condition with respect to the inverse-square weight or some suitable integrability properties. The study of the Almgren frequency function around a point on the edge of the crack, where the domain is highly non-smooth, requires the use of an approximation argument, based on the construction of a sequence of regular sets which approximate the cracked domain. Once a finite limit of the Almgren frequency is shown to exist, a blow-up analysis for scaled solutions allows us to prove asymptotic expansions and strong unique continuation from the edge of the crack. Comment: 32 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2004.11177 Zobrazit plný text záznamu View this record from Arxiv