The obstacle problem for nonlinear elliptic equations with variable growth and L1-data
The aim of this paper is twofold: to prove, for L1-data, the existence and uniqueness of an entropy solution to the obstacle problem for nonlinear elliptic equations with variable growth, and to show some convergence and stability properties of the corresponding coincidence set. The latter follow from extending the Lewy-Stampacchia inequalities to the general framework of L1.
- Diening L, Hästö P, Nekvinda A (2004) Open problems in variable exponent Lebesgue and Sobolev spaces. In: Drabek and Rakosnik (eds) FSDONA04 Proceedings, Milovy, Czech Republic, pp 38–58Google Scholar
- Mosco U (1976) Implicit variational problems and quasi-variational inequalities. Lect Notes Math 543: Berline Heidelberg New York: SpingerGoogle Scholar
- Růžička M (2000) Electrorheological fluids: modeling and mathematical theory. Lect Notes Math 1748. Berlin Heidelberg New York: SpringerGoogle Scholar
- Sanchón M, Urbano JM (2008) Entropy solutions for the p(x)-Laplace equation. Trans Amer Math Soc, to appearGoogle Scholar