Global integrability for weak solutions to some anisotropic elliptic equations. (January 2015) - Innamorati, Alessandra; Leonetti, Francesco
Abstract: We consider the boundary value problem { ∑ i = 1 n D i ( a i ( x, D u ( x ) ) ) = 0, x ∈ Ω ; u ( x ) = u ∗ ( x ), x ∈ ∂ Ω . We show that higher integrability of the boundary datum u ∗ forces solutions u to have higher integrability as well. Assumptions on a i ( x, z ) are suggested by Euler equation of the anisotropic functional ∫ Ω ∑ i = 1 n ( 2 | D i u | 2 + | D i u | sin ( | D i u | ) ) p i 2 .