Finite and infinite energy solutions of singular elliptic problems: Existence and uniqueness

By Francescantonio Oliva, Francesco Petitta. 2016

82 citations recorded by the source corpus.

Abstract We establish existence and uniqueness of solution for the homogeneous Dirichlet problem associated to a fairly general class of elliptic equations modeled by − Δ u = h ( u ) f in Ω , where f is an irregular datum, possibly a measure, and h is a continuous function that may blow up at zero. We also provide regularity results on both the solution and the lower order term depending on the regularity of the data, and we discuss their optimality.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3de5d4ef01004e6ce9278cd575e74659b9231608

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In Applied Mathematics

1. R. Arora
2. Vicentiu D. Rădulescu
3. Dušan D. Repovš
4. Zhijun Zhang
5. Anouar Bahrouni
6. Marius Ghergu
7. V. Ruadulescu
8. K. Kefi

In Computational Theory and Mathematics

1. R. Arora
2. Vicentiu D. Rădulescu
3. Dušan D. Repovš
4. Zhijun Zhang
5. Anouar Bahrouni
6. V. Ruadulescu
7. Marius Ghergu
8. Binlin Zhang

In Mathematical Physics

1. Vicentiu D. Rădulescu
2. R. Arora
3. Zuodong Yang

Citations in the corpus

• Combined effects in mixed local–nonlocal stationary problems (2021, background): “nonlinearities with source terms or absorption terms, we refer to [28, 48, 20, 44] with no intent to furnish an exhaustive list.”