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

Data:	2017
Resum:	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.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Continuity equation ; Rough metrics ; Homogeneous kato square root problem
Publicat a:	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

El registre apareix a les col·leccions:
Articles > Articles publicats > Publicacions matemàtiques
Articles > Articles de recerca