Web of Science: 1 cites, Scopus: 1 cites, Google Scholar: cites
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 ; publishedVersion
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 original: https://www.raco.cat/index.php/PublicacionsMatematiques/article/view/10.5565_PUBLMAT%2061117%2009
DOI: 10.5565/PUBLMAT_61117_09


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