We prove comparison principles for quasilinear elliptic equations whose simplest model islambda u - Delta(p)u + H( x, Du) = 0 x is an element of Omega,where Delta(p)u = div (| Du|(p-2) Du) is the p-Laplace operator with p > 2,. lambda >= 0, H( x,xi) : Omega x R-N -> R is a Caratheodory function and Omega subset of R-N is a bounded domain, N >= 2. We collect several comparison results forweak sub- and super- solutions under different setting of assumptions and with possibly different methods. A strong comparison result is also proved for more regular solutions.
Leonori, T., Porretta, A., Riey, G. (2017). Comparison principles for p-Laplace equations with lower order terms. ANNALI DI MATEMATICA PURA ED APPLICATA, 196(3), 877-903 [10.1007/s10231-016-0600-9].
Comparison principles for p-Laplace equations with lower order terms
Porretta A.;
2017-01-01
Abstract
We prove comparison principles for quasilinear elliptic equations whose simplest model islambda u - Delta(p)u + H( x, Du) = 0 x is an element of Omega,where Delta(p)u = div (| Du|(p-2) Du) is the p-Laplace operator with p > 2,. lambda >= 0, H( x,xi) : Omega x R-N -> R is a Caratheodory function and Omega subset of R-N is a bounded domain, N >= 2. We collect several comparison results forweak sub- and super- solutions under different setting of assumptions and with possibly different methods. A strong comparison result is also proved for more regular solutions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
