We consider a pseudomonotone operator, the model of which is -div(b(x, u)vertical bar del u vertical bar(p-2)del u) with 1 < p < + infinity and b(x, s) a Lipschitz continuous function in s which hold satisfies 0 < alpha <= b(x, s) <= beta < infinity. We show that the comparison principle (and therefore the uniqueness for the Dirichlet problem) in two particular cases, namely the one-dimensional case, and the case where at least one of the right-hand sides does not change sign. To the best of our knowledge these results are new for p > 2. Full detailed proofs are given in the present Note. The results continue to hold when Omega is unbounded.
Casado Diaz, J., Murat, F., Porretta, A. (2007). Uniqueness results for pseudomonotone problems with p > 2. COMPTES RENDUS MATHÉMATIQUE, 344(8), 487-492 [10.1016/j.crma.2007.02.007].
Uniqueness results for pseudomonotone problems with p > 2
PORRETTA, ALESSIO
2007-01-01
Abstract
We consider a pseudomonotone operator, the model of which is -div(b(x, u)vertical bar del u vertical bar(p-2)del u) with 1 < p < + infinity and b(x, s) a Lipschitz continuous function in s which hold satisfies 0 < alpha <= b(x, s) <= beta < infinity. We show that the comparison principle (and therefore the uniqueness for the Dirichlet problem) in two particular cases, namely the one-dimensional case, and the case where at least one of the right-hand sides does not change sign. To the best of our knowledge these results are new for p > 2. Full detailed proofs are given in the present Note. The results continue to hold when Omega is unbounded.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
