Butterfly support for off diagonal coefficients and boundedness of solutions to quasilinear elliptic systems
We consider quasilinear elliptic systems in divergence form. In general, we cannot expect that weak solutions are locally bounded because of De Giorgi’s counterexample. Here we assume that off-diagonal coefficients have a “butterfly support”: this allows us to prove local boundedness of weak solutio...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2021-11-01
|
| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2021-0205 |
| _version_ | 1811185934056554496 |
|---|---|
| author | Leonardi Salvatore Leonetti Francesco Rocha Eugenio Staicu Vasile |
| author_facet | Leonardi Salvatore Leonetti Francesco Rocha Eugenio Staicu Vasile |
| author_sort | Leonardi Salvatore |
| collection | DOAJ |
| description | We consider quasilinear elliptic systems in divergence form. In general, we cannot expect that weak solutions are locally bounded because of De Giorgi’s counterexample. Here we assume that off-diagonal coefficients have a “butterfly support”: this allows us to prove local boundedness of weak solutions. |
| first_indexed | 2024-04-11T13:37:50Z |
| format | Article |
| id | doaj.art-9337ef6d8c9549ecb292083ac007b37f |
| institution | Directory Open Access Journal |
| issn | 2191-9496 2191-950X |
| language | English |
| last_indexed | 2024-04-11T13:37:50Z |
| publishDate | 2021-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-9337ef6d8c9549ecb292083ac007b37f2022-12-22T04:21:24ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2021-11-0111167268310.1515/anona-2021-0205Butterfly support for off diagonal coefficients and boundedness of solutions to quasilinear elliptic systemsLeonardi Salvatore0Leonetti Francesco1Rocha Eugenio2Staicu Vasile3Department of Mathematics and Informatics, University of Catania, Viale A. Doria 6, 95125Catania, ItalyDISIM - Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, Via Vetoio snc - Coppito, 67100, L’Aquila, ItalyCenter for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, PortugalCenter for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, PortugalWe consider quasilinear elliptic systems in divergence form. In general, we cannot expect that weak solutions are locally bounded because of De Giorgi’s counterexample. Here we assume that off-diagonal coefficients have a “butterfly support”: this allows us to prove local boundedness of weak solutions.https://doi.org/10.1515/anona-2021-0205quasilinearellipticsystemweaksolutionregularityprimary: 35j47secondary: 35b6549n60 |
| spellingShingle | Leonardi Salvatore Leonetti Francesco Rocha Eugenio Staicu Vasile Butterfly support for off diagonal coefficients and boundedness of solutions to quasilinear elliptic systems Advances in Nonlinear Analysis quasilinear elliptic system weak solution regularity primary: 35j47 secondary: 35b65 49n60 |
| title | Butterfly support for off diagonal coefficients and boundedness of solutions to quasilinear elliptic systems |
| title_full | Butterfly support for off diagonal coefficients and boundedness of solutions to quasilinear elliptic systems |
| title_fullStr | Butterfly support for off diagonal coefficients and boundedness of solutions to quasilinear elliptic systems |
| title_full_unstemmed | Butterfly support for off diagonal coefficients and boundedness of solutions to quasilinear elliptic systems |
| title_short | Butterfly support for off diagonal coefficients and boundedness of solutions to quasilinear elliptic systems |
| title_sort | butterfly support for off diagonal coefficients and boundedness of solutions to quasilinear elliptic systems |
| topic | quasilinear elliptic system weak solution regularity primary: 35j47 secondary: 35b65 49n60 |
| url | https://doi.org/10.1515/anona-2021-0205 |
| work_keys_str_mv | AT leonardisalvatore butterflysupportforoffdiagonalcoefficientsandboundednessofsolutionstoquasilinearellipticsystems AT leonettifrancesco butterflysupportforoffdiagonalcoefficientsandboundednessofsolutionstoquasilinearellipticsystems AT rochaeugenio butterflysupportforoffdiagonalcoefficientsandboundednessofsolutionstoquasilinearellipticsystems AT staicuvasile butterflysupportforoffdiagonalcoefficientsandboundednessofsolutionstoquasilinearellipticsystems |