Deterministic KPZ-type equations with nonlocal “gradient terms”
The main goal of this paper is to prove existence and non-existence results for deterministic Kardar–Parisi–Zhang type equations involving non-local “gradient terms”. More precisely, let Ω ⊂ RN, N≥ 2 , be a bounded domain with boundary ∂Ω of class C2. For s∈ (0 , 1) , we consider problems of the for...
| Authors: | , , , |
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| Format: | article |
| Publication Date: | 2023 |
| Country: | España |
| Institution: | Universidad Nacional de Educación a Distancia |
| Repository: | e-spacio. Repositorio Institucional de la UNED |
| Language: | English |
| OAI Identifier: | oai:e-spacio.uned.es:20.500.14468/24423 |
| Online Access: | https://hdl.handle.net/20.500.14468/24423 |
| Access Level: | Open access |
| Keyword: | 12 Matemáticas deterministic KPZ–type equations fractional laplacian nonlocal “gradient terms” |
| Summary: | The main goal of this paper is to prove existence and non-existence results for deterministic Kardar–Parisi–Zhang type equations involving non-local “gradient terms”. More precisely, let Ω ⊂ RN, N≥ 2 , be a bounded domain with boundary ∂Ω of class C2. For s∈ (0 , 1) , we consider problems of the form (Formula presented.) where q> 1 and λ> 0 are real parameters, f belongs to a suitable Lebesgue space, μ∈ L∞(Ω) and D represents a nonlocal “gradient term”. Depending on the size of λ> 0 , we derive existence and non-existence results. In particular, we solve several open problems posed in [Abdellaoui in Nonlinearity 31(4): 1260-1298 (2018), Section 6] and [Abdellaoui in Proc Roy Soc Edinburgh Sect A 150(5): 2682-2718 (2020), Section 7]. © 2022, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature. |
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