Geometry of mean value sets for general divergence form uniformly elliptic operators
dc.contributor.author | Aryal, Ashok | |
dc.date.accessioned | 2017-08-04T14:33:35Z | |
dc.date.available | 2017-08-04T14:33:35Z | |
dc.date.graduationmonth | August | en_US |
dc.date.issued | 2017-08-01 | en_US |
dc.date.published | 2017 | en_US |
dc.description.abstract | In the Fermi Lectures on the obstacle problem in 1998, Caffarelli gave a proof of the mean value theorem which extends to general divergence form uniformly elliptic operators. In the general setting, the result shows that for any such operator L and at any point [chi]₀ in the domain, there exists a nested family of sets { D[subscript]r([chi]₀) } where the average over any of those sets is related to the value of the function at [chi]₀. Although it is known that the { D[subscript]r([chi]₀) } are nested and are comparable to balls in the sense that there exists c, C depending only on L such that B[subscript]cr([chi]₀) ⊂ D[subscript]r([chi]₀) ⊂ B[subscript]Cr([chi]₀) for all r > 0 and [chi]₀ in the domain, otherwise their geometric and topological properties are largely unknown. In this work we begin the study of these topics and we prove a few results about the geometry of these sets and give a couple of applications of the theorems. | en_US |
dc.description.advisor | Ivan Blank | en_US |
dc.description.degree | Doctor of Philosophy | en_US |
dc.description.department | Department of Mathematics | en_US |
dc.description.level | Doctoral | en_US |
dc.identifier.uri | http://hdl.handle.net/2097/36205 | |
dc.language.iso | en_US | en_US |
dc.publisher | Kansas State University | en |
dc.subject | Mean value | en_US |
dc.subject | Free boundary | |
dc.title | Geometry of mean value sets for general divergence form uniformly elliptic operators | en_US |
dc.type | Dissertation | en_US |