We prove the existence of a weak solution of the Dirichlet problem for a class of elliptic partial differential systems in separable Orlicz-Sobolev spaces.
An existence theorem for weak solutions for a class of elliptic partial differential systems in general Orlicz–Sobolev spaces
✍ Scribed by Ge Dong
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 258 KB
- Volume
- 69
- Category
- Article
- ISSN
- 0362-546X
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## Abstract We study the existence of solutions of the general elliptic system of partial differential equations in the space where the principal part may be represented with the help of a CLIFFORDalgebra 𝔄. We construct an integral representation and discuss the properties of the kernels.
## Abstract This paper is a continuation of [6]. Here we construct a CAUCHY integral formula and a POMPEJU‐representation for elliptic systems of partial differential equations of first order in __R^n^__, which may be described with the help of a CLIFFORD‐algebra. Moreover we study properties of th