TitleOn some nonlocal elliptic and parabolic equations
NameJin, Tianling (author), Li, YanYan (chair), Han, Zheng-Chao (internal member), Sesum, Natasa (internal member), Sire, Yannick (outside member), Rutgers University, Graduate School - New Brunswick,
Differential equations, Parabolic ,
Differential equations, Elliptic
DescriptionWe prove some results on the existence and compactness of solutions of a fractional Nirenberg problem involving nonlocal conformally invariant operators. Regularity properties for solutions of some degenerate elliptic equations as well as a Liouville type theorem are established, and used in our blow up analysis. We also introduce a fractional Yamabe flow and show that on the conformal spheres it converges to the standard sphere up to a M"obius diffeomorphism. These arguments can be applied to obtain extinction profiles of solutions of some fractional porous medium equations, which are further used to improve a Sobolev inequality via a quantitative estimate of the remainder term.
NoteIncludes bibliographical references
Noteby Tianling Jin
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.