We study the local boundedness of minimizers of non uniformly elliptic integral functionals with a suitable anisotropic p,q- growth condition. More precisely, the growth condition of the integrand function f(x,∇u) from below involves different pi>1 powers of the partial derivatives of u and some monomial weights |xi|αjavax.xml.bind.JAXBElement@2622ea6pjavax.xml.bind.JAXBElement@6159b4dc with αi∈[0,1) that may degenerate to zero. Otherwise from above it is controlled by a q power of the modulus of the gradient of u with q≥maxipi and an unbounded weight μ(x). The main tool in the proof is an anisotropic Sobolev inequality with respect to the weights |xi|αjavax.xml.bind.JAXBElement@1fd02c1apjavax.xml.bind.JAXBElement@3ee15ae7.
Local Boundedness for Minimizers of Anisotropic Functionals with Monomial Weights
Feo F.;Passarelli di Napoli A.;
2024-01-01
Abstract
We study the local boundedness of minimizers of non uniformly elliptic integral functionals with a suitable anisotropic p,q- growth condition. More precisely, the growth condition of the integrand function f(x,∇u) from below involves different pi>1 powers of the partial derivatives of u and some monomial weights |xi|αjavax.xml.bind.JAXBElement@2622ea6pjavax.xml.bind.JAXBElement@6159b4dc with αi∈[0,1) that may degenerate to zero. Otherwise from above it is controlled by a q power of the modulus of the gradient of u with q≥maxipi and an unbounded weight μ(x). The main tool in the proof is an anisotropic Sobolev inequality with respect to the weights |xi|αjavax.xml.bind.JAXBElement@1fd02c1apjavax.xml.bind.JAXBElement@3ee15ae7.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
