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Imbedding estimates and elliptic equations with discontinuous coefficients in unbounded domains. (English) Zbl 0905.35017
Summary: We deal with the multiplication operator $$u\in W^{k,p} (\Omega)\to gu\in L^q (\Omega)$$, with $$g$$ belonging to a space of Morrey type $$M^{r,\lambda} (\Omega)$$. We apply our results in order to establish an a priori bound for the solutions of the Dirichlet problem concerning elliptic equations with discontinuous coefficients.

##### MSC:
 35B45 A priori estimates in context of PDEs 35R05 PDEs with low regular coefficients and/or low regular data 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 35J15 Second-order elliptic equations
##### Keywords:
multiplication operator