Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 39, pp. 1-17.
Title: Regular oblique derivative problem in Morrey spaces
Authors: Dian K. Palagachev (Politecnico di Bari, Bari, Italy)
Maria Alessandra Ragusa (Univ. di Catania, Catania, Italy)
Lubomira G. Softova (Bulgarian Academy of Sciences, Sofia, Bulgaria)
Abstract:
This article presents a study of the regular oblique derivative problem
$$ \displaylines{
\sum_{i,j=1}^n a^{ij}(x) \frac{\partial^2 u }{\partial x_i\partial x_j} =f(x) \cr
\frac{\partial u }{\partial \ell(x)}+ \sigma(x) u = \varphi(x)\,.
}$$
Assuming that the coefficients $a^{ij}$ belong to the Sarason's class
of functions with vanishing mean oscillation, we show existence and
global regularity of strong solutions in Morrey spaces.
Submitted December 17, 1999. Published May 23, 2000.
Math Subject Classifications: 35J25, 35B65, 35R05
Key Words: Uniformly elliptic operator; regular oblique derivative problem;
Morrey spaces.