Electron. J. Diff. Eqns., Vol. 2000(2000), No. 39, pp. 1-17.

Regular oblique derivative problem in Morrey spaces

Dian K. Palagachev, Maria Alessandra Ragusa, & Lubomira G. Softova

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.

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Dian K. Palagachev
Dipartimento Interuniversitario di Matematica
Politecnico di Bari,
Via E. Orabona, 4, 70125 Bari, Italy
email: dian@pascal.dm.uniba.it
Maria Alessandra Ragusa
Dipartimento di Matematica, Universita di Catania,
Viale A. Doria, 6, 95125 Catania, Italy
email: maragusa@dipmat.unict.it
Lubomira G. Softova
Bulgarian Academy of Sciences
Institute of Mathematics and Informatics, Dept. Math. Physics,
``Acad. G. Bonchev'' Str., bl. 8, 1113 Sofia, Bulgaria
email: luba@dipmat.unict.it

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