Remarks on the decay/growth rate of solutions to elliptic free boundary problems of obstacle type
The purpose of this note is to present a “new” approach to the decay rate of the solutions to the no-sign obstacle problem from the free boundary, based on Weiss-monotonicity formula. In presenting the approach we have chosen to treat a problem which is not touched earlier in the existing literature...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2020-10-01
|
| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/mine.2020032/fulltext.html |
| _version_ | 1818149657075777536 |
|---|---|
| author | Morteza Fotouhi Andreas Minne Henrik Shahgholian Georg S. Weiss |
| author_facet | Morteza Fotouhi Andreas Minne Henrik Shahgholian Georg S. Weiss |
| author_sort | Morteza Fotouhi |
| collection | DOAJ |
| description | The purpose of this note is to present a “new” approach to the decay rate of the solutions to the no-sign obstacle problem from the free boundary, based on Weiss-monotonicity formula. In presenting the approach we have chosen to treat a problem which is not touched earlier in the existing literature. Although earlier techniques may still work for this problem, we believe this approach gives a shorter proof, and may have wider applications. |
| first_indexed | 2024-12-11T13:10:31Z |
| format | Article |
| id | doaj.art-50c8b68809574157b770d105fe7c927c |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-12-11T13:10:31Z |
| publishDate | 2020-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-50c8b68809574157b770d105fe7c927c2022-12-22T01:06:12ZengAIMS PressMathematics in Engineering2640-35012020-10-012469870810.3934/mine.2020032Remarks on the decay/growth rate of solutions to elliptic free boundary problems of obstacle typeMorteza Fotouhi0Andreas Minne1Henrik Shahgholian2Georg S. Weiss31 Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran2 Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden2 Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden3 Department of Mathematics, University of Duisburg-Essen, Essen, GermanyThe purpose of this note is to present a “new” approach to the decay rate of the solutions to the no-sign obstacle problem from the free boundary, based on Weiss-monotonicity formula. In presenting the approach we have chosen to treat a problem which is not touched earlier in the existing literature. Although earlier techniques may still work for this problem, we believe this approach gives a shorter proof, and may have wider applications.https://www.aimspress.com/article/10.3934/mine.2020032/fulltext.htmlno-sign obstacle problemsingular elliptic equationregularity of solutions |
| spellingShingle | Morteza Fotouhi Andreas Minne Henrik Shahgholian Georg S. Weiss Remarks on the decay/growth rate of solutions to elliptic free boundary problems of obstacle type Mathematics in Engineering no-sign obstacle problem singular elliptic equation regularity of solutions |
| title | Remarks on the decay/growth rate of solutions to elliptic free boundary problems of obstacle type |
| title_full | Remarks on the decay/growth rate of solutions to elliptic free boundary problems of obstacle type |
| title_fullStr | Remarks on the decay/growth rate of solutions to elliptic free boundary problems of obstacle type |
| title_full_unstemmed | Remarks on the decay/growth rate of solutions to elliptic free boundary problems of obstacle type |
| title_short | Remarks on the decay/growth rate of solutions to elliptic free boundary problems of obstacle type |
| title_sort | remarks on the decay growth rate of solutions to elliptic free boundary problems of obstacle type |
| topic | no-sign obstacle problem singular elliptic equation regularity of solutions |
| url | https://www.aimspress.com/article/10.3934/mine.2020032/fulltext.html |
| work_keys_str_mv | AT mortezafotouhi remarksonthedecaygrowthrateofsolutionstoellipticfreeboundaryproblemsofobstacletype AT andreasminne remarksonthedecaygrowthrateofsolutionstoellipticfreeboundaryproblemsofobstacletype AT henrikshahgholian remarksonthedecaygrowthrateofsolutionstoellipticfreeboundaryproblemsofobstacletype AT georgsweiss remarksonthedecaygrowthrateofsolutionstoellipticfreeboundaryproblemsofobstacletype |