Continuity of solutions to space-varying pointwise linear elliptic equations
Bandara, Lashi (Chalmers University of Technology (Suècia))

Date:	2017
Abstract:	We consider pointwise linear elliptic equations of the form Lα uα = ŋα on a smooth compact manifold where the operators Lα are in divergence form with real, bounded, measurable coefficients that vary in the space variableα. We establish L2-continuity of the solutions at α whenever the coefficients of Lα are L∞ -continuous at α and the initial datum is L2 -continuous at α. This is obtained by reducing the continuity of solutions to a homogeneous Kato square root problem. As an application, we consider a time evolving family of metrics gt that is tangential to the Ricci flow almost-everywhere along geodesics when starting with a smooth initial metric. Under the assumption that our initial metric is a rough metric on ʍ with a C1 heat kernel on a "non-singular" nonempty open subset Ɲ, we show that α à gt (α) is continuous whenever α € Ɲ.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Continuity equation ; Rough metrics ; Homogeneous kato square root problem
Published in:	Publicacions matemàtiques, Vol. 61 Núm. 1 (2017) , p. 239-258 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/316085
DOI: 10.5565/PUBLMAT_61117_09

20 p, 413.2 KB

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