Murray State Theses and Dissertations


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 W1,pD is a weak solution to the eigenvalue problem, then u also belongs to W1,pD 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


Year degree awarded


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.pdf (293 kB)

Included in

Analysis Commons