Comparison results for nonlinear divergence structure elliptic PDE’s
First we prove a comparison result for a nonlinear divergence structure elliptic partial differential equation. Next we find an estimate of the solution of a boundary value problem in a domain Ω in terms of the solution of a related symmetric boundary value problem in a ball B having the same measur...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2019-06-01
|
| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2020-0008 |
| _version_ | 1818715872243482624 |
|---|---|
| author | Liu Yichen Marras Monica Porru Giovanni |
| author_facet | Liu Yichen Marras Monica Porru Giovanni |
| author_sort | Liu Yichen |
| collection | DOAJ |
| description | First we prove a comparison result for a nonlinear divergence structure elliptic partial differential equation. Next we find an estimate of the solution of a boundary value problem in a domain Ω in terms of the solution of a related symmetric boundary value problem in a ball B having the same measure as Ω. For p-Laplace equations, the corresponding result is due to Giorgio Talenti. In a special (radial) case we also prove a reverse comparison result. |
| first_indexed | 2024-12-17T19:10:16Z |
| format | Article |
| id | doaj.art-e7ab63efca224e69bd7f63ca5d374183 |
| institution | Directory Open Access Journal |
| issn | 2191-950X |
| language | English |
| last_indexed | 2024-12-17T19:10:16Z |
| publishDate | 2019-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-e7ab63efca224e69bd7f63ca5d3741832022-12-21T21:35:53ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2019-06-019143844810.1515/anona-2020-0008anona-2020-0008Comparison results for nonlinear divergence structure elliptic PDE’sLiu Yichen0Marras Monica1Porru Giovanni2Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, Suzhou, ChinaDepartment of Mathematics and Informatics, University of Cagliari, Cagliari, ItalyDepartment of Mathematics and Informatics, University of Cagliari, Cagliari, ItalyFirst we prove a comparison result for a nonlinear divergence structure elliptic partial differential equation. Next we find an estimate of the solution of a boundary value problem in a domain Ω in terms of the solution of a related symmetric boundary value problem in a ball B having the same measure as Ω. For p-Laplace equations, the corresponding result is due to Giorgio Talenti. In a special (radial) case we also prove a reverse comparison result.https://doi.org/10.1515/anona-2020-0008quasi-linear equationssymmetrizationcomparison results35b5135j6249k2049k30 |
| spellingShingle | Liu Yichen Marras Monica Porru Giovanni Comparison results for nonlinear divergence structure elliptic PDE’s Advances in Nonlinear Analysis quasi-linear equations symmetrization comparison results 35b51 35j62 49k20 49k30 |
| title | Comparison results for nonlinear divergence structure elliptic PDE’s |
| title_full | Comparison results for nonlinear divergence structure elliptic PDE’s |
| title_fullStr | Comparison results for nonlinear divergence structure elliptic PDE’s |
| title_full_unstemmed | Comparison results for nonlinear divergence structure elliptic PDE’s |
| title_short | Comparison results for nonlinear divergence structure elliptic PDE’s |
| title_sort | comparison results for nonlinear divergence structure elliptic pde s |
| topic | quasi-linear equations symmetrization comparison results 35b51 35j62 49k20 49k30 |
| url | https://doi.org/10.1515/anona-2020-0008 |
| work_keys_str_mv | AT liuyichen comparisonresultsfornonlineardivergencestructureellipticpdes AT marrasmonica comparisonresultsfornonlineardivergencestructureellipticpdes AT porrugiovanni comparisonresultsfornonlineardivergencestructureellipticpdes |