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EnglishWe consider nonlinear elliptic equations driven by a nonhomogeneous differential operator plus an indefinite potential. The boundary condition is either Dirichlet or Robin (including as a special case the Neumann problem). First we present the corresponding regularity theory (up to the boundary). Then we develop the nonlinear maximum principle and present some important nonlinear strong comparison principles. Subsequently we see how these results together with variational methods, truncation and perturbation techniques, and Morse theory (critical groups) can be used to analyze different classes of elliptic equations. Special attention is given to (p, 2)-equations (these are equations driven by the sum of a p- Laplacian and a Laplacian), where stronger results can be stated.
Papageorgiou N.S., Vetro C., & Vetro F. (2019). Nonlinear nonhomogeneous elliptic problems. In Dutta Hemen, Kočinac Ljubiša D. R., & Srivastava Hari M. (a cura di), Current Trends in Mathematical Analysis and its Interdisciplinary Applications (pp. 647-713). Springer International Publishing [10.1007/978-3-030-15242-0_17].
| Data di pubblicazione: | 2019 | |
| Titolo: | Nonlinear nonhomogeneous elliptic problems | |
| Autori: | ||
| Citazione: | Papageorgiou N.S., Vetro C., & Vetro F. (2019). Nonlinear nonhomogeneous elliptic problems. In Dutta Hemen, Kočinac Ljubiša D. R., & Srivastava Hari M. (a cura di), Current Trends in Mathematical Analysis and its Interdisciplinary Applications (pp. 647-713). Springer International Publishing [10.1007/978-3-030-15242-0_17]. | |
| Abstract: | We consider nonlinear elliptic equations driven by a nonhomogeneous differential operator plus an indefinite potential. The boundary condition is either Dirichlet or Robin (including as a special case the Neumann problem). First we present the corresponding regularity theory (up to the boundary). Then we develop the nonlinear maximum principle and present some important nonlinear strong comparison principles. Subsequently we see how these results together with variational methods, truncation and perturbation techniques, and Morse theory (critical groups) can be used to analyze different classes of elliptic equations. Special attention is given to (p, 2)-equations (these are equations driven by the sum of a p- Laplacian and a Laplacian), where stronger results can be stated. | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/978-3-030-15242-0_17 | |
| URL: | https://www.springer.com/us/book/9783030152413#aboutBook | |
| Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica | |
| Appare nelle tipologie: | 2.01 Capitolo o Saggio |
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