4 papers
math.AP2008
The mixed problem for harmonic functions in polyhedra
Moises Venouziou, Gregory C. Verchota
R. M. Brown's theorem on mixed Dirichlet and Neumann boundary conditions is extended in two ways for the special case of polyhedral domains. A (1) more general partition of the bou…
math.AG2007
Existence of positive definite noncoercive sums of squares
Gregory C. Verchota
Positive definite forms which are sums of squares are constructed to have the additional property that the members of any collection of forms whose squares sum to must shar…
math.AP2001
On the biharmonic Dirichlet problem: The higher dimensional case
Atanas Stefanov, Gregory C. Verchota
Withdrawn by authors.
math.CA2000
Optimal solvability for the Dirichlet and Neumann problem in dimension two
Atanas Stefanov, Gregory Verchota
We show existence and uniqueness for the solutions of the regularity and the Neumann problems for harmonic functions on Lipschitz domains with data in the Hardy spaces H^p, p>2/3,…