Imbedding estimates and elliptic equations with discontinuous coefficients in unbounded domains. (English) Zbl 0905.35017

Cavaliere, Paola; Longobardi, Maria; Vitolo, Antonio

Matematiche 51, No. 1, 87-104 (1996).

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