Nonlinear anisotropic elliptic and parabolic equations with variable exponents and L1 data

We prove existence and regularity results for distributional solutions of nonlinear elliptic and parabolic equations with general anisotropic diffusivities with variable exponents. The data are assumed to be merely integrable.

[1]  M. Bendahmane,et al.  Renormalized solutions for a nonlinear parabolic equation with variable exponents and l(1)-data , 2010 .

[2]  José Miguel Urbano,et al.  Entropy solutions for the p(x)-Laplace equation , 2009 .

[3]  M. Bendahmane,et al.  Renormalized solutions for nonlinear elliptic equations with variable exponents and L1 data , 2009 .

[4]  Fengquan Li.  Anisotropic parabolic equations with measure data II , 2006 .

[5]  Yunmei Chen,et al.  Variable Exponent, Linear Growth Functionals in Image Restoration , 2006, SIAM J. Appl. Math..

[6]  Peter Hästö,et al.  The Dirichlet Energy Integral and Variable Exponent Sobolev Spaces with Zero Boundary Values , 2006 .

[7]  Mazen Saad,et al.  On some anisotropic reaction-diffusion systems with L1-data modeling the propagation of an epidemic disease , 2003 .

[8]  Xianling Fan,et al.  On the Spaces Lp(x)(Ω) and Wm, p(x)(Ω) , 2001 .

[9]  Xianling Fan,et al.  Sobolev Embedding Theorems for Spaces Wk, p(x)(Ω) , 2001 .

[10]  Giuseppe Mingione,et al.  Regularity Results for a Class of Functionals with Non-Standard Growth , 2001 .

[11]  Lucio Boccardo,et al.  Anisotropic equations in $L^1$ , 1996, Differential and Integral Equations.

[12]  T. Gallouët,et al.  Non-linear elliptic and parabolic equations involving measure data , 1989 .

[13]  Paolo Marcellini.  Regularity of minimizers of integrals of the calculus of variations with non standard growth conditions , 1989 .

[14]  J. Simon.  Compact sets in the spaceLp(O,T; B) , 1986 .

[15]  V. Zhikov.  Density of Smooth Functions in Sobolev-Orlicz Spaces , 2006 .

[16]  Jacques Simeon,et al.  Compact Sets in the Space L~(O, , 2005 .

[17]  M. Ruzicka,et al.  Electrorheological Fluids: Modeling and Mathematical Theory , 2000 .

[18]  Jiří Rákosník,et al.  On spaces $L^{p(x)}$ and $W^{k, p(x)}$ , 1991 .