Multiple blowing-up solutions to critical elliptic systems in bounded domains
| Autor: | Kim, Seunghyeok, Pistoia, Angela |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | We construct families of blowing-up solutions to elliptic systems on smooth bounded domains in the Euclidean space, which are variants of the critical Lane-Emden system and analogous to the Brezis-Nirenberg problem. We find a function which governs blowing-up points and rates, observing that it reflects the strong nonlinear characteristic of the system. By using it, we also prove that a single blowing-up solution exists in general domains, and construct examples of contractible domains where multiple blowing-up solutions are allowed to exist. We believe that a variety of new ideas and arguments developed here will help to analyze blowing-up phenomena in related Hamiltonian-type systems. Comment: 40 pages, minor revision (typo fixed, grant information updated) |
| Databáze: | arXiv |
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