Abstract
We show that bounded solutions of the quasilinear elliptic equation \(\Delta_{p(x)} u=g+div(\textbf{F})\) are locally Hölder continuous provided that the functions \(g\) and \(\textbf{F}\) are in suitable Lebesgue spaces.
Publisher
University of Zagreb, Faculty of Science, Department of Mathematics
Reference25 articles.
1. E. Acerbi and G. Mingione, Gradient estimates for the \(p(x)\)-Laplacean system, J. Reine Angew. Math. 584 (2005), 117-148.
2. S. Antontsev and S. Shmarev, Elliptic equations with anisotropic nonlinearity and nonstandard growth conditions, in: Handbook of differential equations: Stationary partial differential equations, Vol 3, Elsevier-North Holland, 2006, 1-100.
3. A. Coscia and G. Mingione, Hölder continuity of the gradient of \(p(x)\)-harmonic mappings, C. R. Acad. Sci. Paris Sér. I Math. 328, (1999), 363-368.
4. J. Carrillo and A. Lyaghfouri, The dam problem for nonlinear Darcy's laws and Dirichlet boundary conditions, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 26 (1998), 453-505.
5. S. Challal and A. Lyaghfouri, A filtration problem through a heterogeneous porous medium, Interfaces Free Bound. 6 (2004), 55-79.