The Existence and Uniqueness of Nonlinear Elliptic Equations with General Growth in the Gradient

Angelo Alvino, Vincenzo Ferone and Anna Mercaldo ()
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Angelo Alvino: Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli Federico II, 80138 Napoli, Italy
Vincenzo Ferone: Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli Federico II, 80138 Napoli, Italy
Anna Mercaldo: Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli Federico II, 80138 Napoli, Italy

Mathematics, 2024, vol. 13, issue 1, 1-14

Abstract: In this paper, we prove the existence and uniqueness results for a weak solution to a class of Dirichlet boundary value problems whose prototype is − Δ p u = β | ∇ u | q + f i n Ω , u = 0 o n ∂ Ω , where Ω is a bounded open subset of R N , N ≥ 2 , 1 < p < N , Δ p u = div | ∇ u | p − 2 ∇ u , p − 1 < q < p , β is a positive constant and f is a measurable function satisfying suitable summability conditions depending on q and a smallness condition.

Keywords: uniqueness; nonlinear elliptic equations; existence; a priori estimates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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