Existence and boundary asymptotic behavior of large solutions of Hessian equations

Ma, Shanshan; Li, Dongsheng

doi:10.1016/j.na.2019.03.021

Cited by 9 publications

(2 citation statements)

References 26 publications

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“…More results on the existence, uniqueness and asymptotic behavior of boundary blow-up solutions to (1.1) in the bounded domain see [5,8,10,16,20,22,25]. Other works of entire solutions to the Monge-Ampère or Hessian equation, see [4,7,11,26].…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

Global existence and asymptotic behavior of solutions to fractional (p,q)-Laplacian equations

Song

Quan

et al. 2021

Asymptotic Analysis

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The aim of this paper is to consider the following fractional parabolic problem u t + ( − Δ ) p α u + ( − Δ ) q β u = f ( x , u ) ( x , t ) ∈ Ω × ( 0 , ∞ ) , u = 0 ( x , t ) ∈ ( R N ∖ Ω ) × ( 0 , ∞ ) , u ( x , 0 ) = u 0 ( x ) x ∈ Ω , where Ω ⊂ R N is a bounded domain with Lipschitz boundary, ( − Δ ) p α is the fractional p-Laplacian with 0 < α < 1 < p < ∞, ( − Δ ) q β is the fractional q-Laplacian with 0 < β < α < 1 < q < p < ∞, r > 1 and λ > 0. The global existence of nonnegative solutions is obtained by combining the Galerkin approximations with the potential well theory. Then, by virtue of a differential inequality technique, we give a decay estimate of solutions.

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Section: Introduction and The Main Resultsmentioning

confidence: 99%

Global existence and asymptotic behavior of solutions to fractional (p,q)-Laplacian equations

Song

Quan

et al. 2021

Asymptotic Analysis

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“…This result was later generalized to Hessian equations by Huang in [14], and was generalized to Monge-Ampère equations with weight by Zhang, Du-Zhang in [9,26,28]. See also [10,20,27] for some other extensions. The first part of this paper is devoted to prove the counterpart of Theorem 1.1 as following.…”

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confidence: 99%

Euclidean Complete Hypersurfaces of a Monge-Ampere Equation

Du¹

2021

Preprint

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We study the Monge-Ampère Equation (0.1) det D 2 u = u p , ∀x ∈ Ω for some p ∈ R. A solution u of (0.1) is called to be Euclidean complete if it is an entire solution defined over the whole R n or its graph is a large hypersurface satisfying the large conditionIn this paper, we will give various sharp conditions on p and Ω classifying the Euclidean complete solution of (0.1). Our results clarify and extend largely the existence theorem of Cirstea-Trombetti (Calc. Var., 31, 2008, 167-186) for bounded convex domain and p > n.

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The Optimal Global Estimates and Boundary Behavior for Large Solutions to the k-Hessian Equation

Wan

Shi²

2023

Front. Math

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Existence and boundary asymptotic behavior of large solutions of Hessian equations

Abstract: In this paper, we establish the existence of large solutions of Hessian equations and obtain a new boundary asymptotic behavior of solutions.

Cited by 9 publications

References 26 publications

Global existence and asymptotic behavior of solutions to fractional (p,q)-Laplacian equations

Global existence and asymptotic behavior of solutions to fractional (p,q)-Laplacian equations

Euclidean Complete Hypersurfaces of a Monge-Ampere Equation

The Optimal Global Estimates and Boundary Behavior for Large Solutions to the k-Hessian Equation

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