W^1,p Regularity of Eigenfunctions for the Mixed Problem with Nonhomogeneous Neumann Data

Author

Kohei Miyazaki, Murray State UniversityFollow

Abstract

We consider an eigenvalue problem with a mixed boundary condition, where a second-order differential operator is given in divergence form and satisfies a uniform ellipticity condition. We show that if a function u in the Sobolev space W^1,p_D is a weak solution to the eigenvalue problem, then u also belongs to W^1,p_D for some p>2. To do so, we show a reverse Hölder inequality for the gradient of u. The decomposition of the boundary is assumed to be such that we get both Poincaré and Sobolev-type inequalities up to the boundary.

Year manuscript completed

2018

Year degree awarded

2018

Author's Keywords

Eigenvalues, elliptic equations, Sobolev spaces, partial differential equations

Thesis Advisor

Justin Taylor

Committee Chair

Justin Taylor

Committee Member

Maeve McCarthy

Committee Member

Renee Fister

Document Type

Thesis

Recommended Citation

Miyazaki, Kohei, "W^1,p Regularity of Eigenfunctions for the Mixed Problem with Nonhomogeneous Neumann Data" (2018). Murray State Theses and Dissertations. 100.
https://digitalcommons.murraystate.edu/etd/100