Existence of bounded solutions for a class of singular elliptic problems involving the 1-Laplacian operator

In this work we study existence and regularity of solutions to problems which are modeled by - Δ p u + u | ∇ u | p = f h ( u ) in Ω , u = 0 on ∂ Ω . Here Ω is an open bounded subset of R N ( N ≥ 2 ) with Lipschitz boundary, Δ p u : = div ( | ∇ u | p - 2 ∇ u ) ( 1 ≤ p < N ) is the p-Laplacian oper...

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Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2023-07, Vol.117 (3), Article 111
Main Authors: El Hichami, Mohamed, El Hadfi, Youssef
Format: Article
Language:English
Subjects:
Applications of Mathematics
Continuity (mathematics)
Laplace transforms
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operators (mathematics)
Original Paper
Theoretical
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Summary:In this work we study existence and regularity of solutions to problems which are modeled by - Δ p u + u | ∇ u | p = f h ( u ) in Ω , u = 0 on ∂ Ω . Here Ω is an open bounded subset of R N ( N ≥ 2 ) with Lipschitz boundary, Δ p u : = div ( | ∇ u | p - 2 ∇ u ) ( 1 ≤ p < N ) is the p-Laplacian operator, f ∈ L q ( Ω ) ( q > N p ) is a nonnegative function and h is a continuous real function that may possibly blow up at zero.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-023-01444-4