In this paper we deal with large solutions to {−Δ+|∇|=()=+∞ in Ω, on ∂Ω, where Ω⊂ℝ , with ≥1, is a smooth, open, connected, and bounded domain, ≥2, >0, −1<≤ and ∈(Ω)∩∞(Ω). We are interested in studying their behavior as p diverges. Our main result states that, if, in some sense, the domain Ω is large enough, such solutions converge locally uniformly to a limit function that turns out to be a large solution of a suitable limit equation (that involves the ∞-Laplacian). Otherwise, if Ω is small, we have a complete blow-up.

Large solutions to quasilinear problems involving the p-Laplacian as p diverges / Buccheri, Stefano; Leonori, Tommaso. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 60:1(2021). [10.1007/s00526-020-01883-6]

Large solutions to quasilinear problems involving the p-Laplacian as p diverges

Buccheri, Stefano;Leonori, Tommaso
2021

Abstract

In this paper we deal with large solutions to {−Δ+|∇|=()=+∞ in Ω, on ∂Ω, where Ω⊂ℝ , with ≥1, is a smooth, open, connected, and bounded domain, ≥2, >0, −1<≤ and ∈(Ω)∩∞(Ω). We are interested in studying their behavior as p diverges. Our main result states that, if, in some sense, the domain Ω is large enough, such solutions converge locally uniformly to a limit function that turns out to be a large solution of a suitable limit equation (that involves the ∞-Laplacian). Otherwise, if Ω is small, we have a complete blow-up.
Large solutions
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Large solutions to quasilinear problems involving the p-Laplacian as p diverges / Buccheri, Stefano; Leonori, Tommaso. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 60:1(2021). [10.1007/s00526-020-01883-6]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1604552
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