Master of Science / Department of Mathematics / Ivan Blank / Charles N. Moore / This paper will examine some mathematical properties and models of inhomogeneous
materials. By deriving models for elastic energy and heat flow we are
able to establish equations that arise in the study of divergence form uniformly elliptic
partial differential equations. In the late 1950's DeGiorgi and Nash
showed that weak solutions to our partial differential equation lie in the
Holder class.
After fixing the dimension of the space,
the Holder exponent guaranteed by this work depends only on
the ratio of the eigenvalues.
In this paper we will look at a specific geometry and show
that the Holder exponent
of the actual solutions is bounded away from
zero independent of the eigenvalues.
| Identifer | oai:union.ndltd.org:KSU/oai:krex.k-state.edu:2097/900 |
| Date | January 1900 |
| Creators | Kinkade, Kyle Richard |
| Publisher | Kansas State University |
| Source Sets | K-State Research Exchange |
| Detected Language | English |
| Type | Report |
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