Affiliation:
1. Sapienza Università di Roma, Italy
Abstract
We study existence and regularity of weak solutions for a class of boundary value problems, whose form is − div ( log ( 1 + | ∇ u | ) | ∇ u | m ( x ) ∇ u ) + u | ∇ u | log ( 1 + | ∇ u | ) = f ( x ) , in Ω u = 0 , on ∂ Ω where both the principal part and the lower order term have a logarithmic growth with respect to the gradient of the solutions. We prove that the solutions, due to the regularizing effect given by the lower order term, belong to the Orlicz–Sobolev space generated by the function s log ( 1 + | s | ) even for L 1 ( Ω ) data.
Reference14 articles.
1. A contribution to the theory of quasilinear elliptic equations and application to the minimization of integral functionals;Boccardo;Milan Journal of Mathematics,2017
2. Strongly nonlinear elliptic equations having natural growth terms and L 1 data;Boccardo;Nonlinear Anal.,1992
3. L ∞ estimate for some nonlinear elliptic partial differential equations and application to an existence result;Boccardo;SIAM J. Math. Anal.,1992
4. Leray–Lions operators with logarithmic growth;Boccardo;Journal of Mathematical Analysis and Applications.,2015
5. Regularity for non-autonomous functionals with almost linear growth;Breit;Manuscripta Math.,2011