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.
2007
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - ANALISI MATEMATICA
English
NONLINEAR ELLIPTIC-EQUATIONS; OPERATORS
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].
Casado Diaz, J; Murat, F; Porretta, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/34891
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