Maximum principles for viscosity solutions of weakly elliptic equations
Maximum principles play an important role in the theory of elliptic equations. In the last decades there have been many contributions related to the development of fully nonlinear equations and viscosity solutions. Here we consider degenerate elliptic equations, where the main term is a partial tra...
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| Format: | Article |
| Language: | English |
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University of Bologna
2019-12-01
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| Series: | Bruno Pini Mathematical Analysis Seminar |
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| Online Access: | https://mathematicalanalysis.unibo.it/article/view/10395 |
| _version_ | 1811330494443290624 |
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| author | Antonio Vitolo |
| author_facet | Antonio Vitolo |
| author_sort | Antonio Vitolo |
| collection | DOAJ |
| description | Maximum principles play an important role in the theory of elliptic equations. In the last decades there have been many contributions related to the development of fully nonlinear equations and viscosity solutions. Here we consider degenerate elliptic equations, where the main term is a partial trace of the Hessian matrix of the solution. We establish maximum principles in domains that are unbounded in some directions, contained in slabs, and extended maximum principles, which lead to removable singularity results. |
| first_indexed | 2024-04-13T16:02:36Z |
| format | Article |
| id | doaj.art-f3610dac4b6843139e57ec1baac1c731 |
| institution | Directory Open Access Journal |
| issn | 2240-2829 |
| language | English |
| last_indexed | 2024-04-13T16:02:36Z |
| publishDate | 2019-12-01 |
| publisher | University of Bologna |
| record_format | Article |
| series | Bruno Pini Mathematical Analysis Seminar |
| spelling | doaj.art-f3610dac4b6843139e57ec1baac1c7312022-12-22T02:40:29ZengUniversity of BolognaBruno Pini Mathematical Analysis Seminar2240-28292019-12-0110111013610.6092/issn.2240-2829/103958817Maximum principles for viscosity solutions of weakly elliptic equationsAntonio Vitolo0Dipartimento di Ingegneria Civile, Università di Salerno.Maximum principles play an important role in the theory of elliptic equations. In the last decades there have been many contributions related to the development of fully nonlinear equations and viscosity solutions. Here we consider degenerate elliptic equations, where the main term is a partial trace of the Hessian matrix of the solution. We establish maximum principles in domains that are unbounded in some directions, contained in slabs, and extended maximum principles, which lead to removable singularity results.https://mathematicalanalysis.unibo.it/article/view/10395weighted partial trace operatorsfully nonlinear elliptic equationsviscosity solutionsholder estimates |
| spellingShingle | Antonio Vitolo Maximum principles for viscosity solutions of weakly elliptic equations Bruno Pini Mathematical Analysis Seminar weighted partial trace operators fully nonlinear elliptic equations viscosity solutions holder estimates |
| title | Maximum principles for viscosity solutions of weakly elliptic equations |
| title_full | Maximum principles for viscosity solutions of weakly elliptic equations |
| title_fullStr | Maximum principles for viscosity solutions of weakly elliptic equations |
| title_full_unstemmed | Maximum principles for viscosity solutions of weakly elliptic equations |
| title_short | Maximum principles for viscosity solutions of weakly elliptic equations |
| title_sort | maximum principles for viscosity solutions of weakly elliptic equations |
| topic | weighted partial trace operators fully nonlinear elliptic equations viscosity solutions holder estimates |
| url | https://mathematicalanalysis.unibo.it/article/view/10395 |
| work_keys_str_mv | AT antoniovitolo maximumprinciplesforviscositysolutionsofweaklyellipticequations |