Bulletin of the Belgian Mathematical Society - Simon Stevin

An existence result for nonlinear elliptic equations in Musielak-Orlicz-Sobolev spaces

A. Benkirane and M. Sidi El Vally

Full-text: Open access

Abstract

In this paper we prove an existence result for some class of variational boundary value problems for quasilinear elliptic equations in the Musielak-Orlicz spaces $W^mL_\varphi(\Omega)$, under the assumption that the conjugate function of $\varphi$ satisfies the $\Delta_2$ condition. An imbedding theorem has also been provided without assuming this condition.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 20, Number 1 (2013), 57-75.

Dates
First available in Project Euclid: 18 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1366306714

Digital Object Identifier
doi:10.36045/bbms/1366306714

Mathematical Reviews number (MathSciNet)
MR3082743

Zentralblatt MATH identifier
1278.35101

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 46A80: Modular spaces 35J40: Boundary value problems for higher-order elliptic equations

Keywords
Musielak-Orlicz-Sobolev spaces elliptic boundary value problem $\varphi$-Laplacian Musielak-Orlicz function compact imbedding

Citation

Benkirane, A.; Sidi El Vally, M. An existence result for nonlinear elliptic equations in Musielak-Orlicz-Sobolev spaces. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 1, 57--75. doi:10.36045/bbms/1366306714. https://projecteuclid.org/euclid.bbms/1366306714


Export citation