Necessary and sufficient conditions for Hölder continuity of solutions of degenerate Schrödinger operators
In this paper it is studied the Hoelder-continuity of solutions of a linear degenerate elliptic equation of the form<br /> (∗) <em> -Sum_ {i, j =1}^n (a_{i j} u_{x_i} )_{x_j} + V u = 0</em>.<br />It is proved that the solutions of (∗) are Hoelder-continuous...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Università degli Studi di Catania
1997-11-01
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| Series: | Le Matematiche |
| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/418 |
| _version_ | 1818505429290844160 |
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| author | Carmela Vitanza Pietro Zamboni |
| author_facet | Carmela Vitanza Pietro Zamboni |
| author_sort | Carmela Vitanza |
| collection | DOAJ |
| description | In this paper it is studied the Hoelder-continuity of solutions of a linear degenerate elliptic equation of the form<br /> (∗) <em> -Sum_ {i, j =1}^n (a_{i j} u_{x_i} )_{x_j} + V u = 0</em>.<br />It is proved that the solutions of (∗) are Hoelder-continuous if the coefficient V belongs to an appropriate "degenerate" Morrey space. Under some additional assumptions on the weight giving the degeneracy, the previous condition is also necessary. |
| first_indexed | 2024-12-10T21:50:39Z |
| format | Article |
| id | doaj.art-2b9180e790a24c2bac1b299f303c4756 |
| institution | Directory Open Access Journal |
| issn | 0373-3505 2037-5298 |
| language | English |
| last_indexed | 2024-12-10T21:50:39Z |
| publishDate | 1997-11-01 |
| publisher | Università degli Studi di Catania |
| record_format | Article |
| series | Le Matematiche |
| spelling | doaj.art-2b9180e790a24c2bac1b299f303c47562022-12-22T01:32:13ZengUniversità degli Studi di CataniaLe Matematiche0373-35052037-52981997-11-01522393409390Necessary and sufficient conditions for Hölder continuity of solutions of degenerate Schrödinger operatorsCarmela VitanzaPietro ZamboniIn this paper it is studied the Hoelder-continuity of solutions of a linear degenerate elliptic equation of the form<br /> (∗) <em> -Sum_ {i, j =1}^n (a_{i j} u_{x_i} )_{x_j} + V u = 0</em>.<br />It is proved that the solutions of (∗) are Hoelder-continuous if the coefficient V belongs to an appropriate "degenerate" Morrey space. Under some additional assumptions on the weight giving the degeneracy, the previous condition is also necessary.http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/418 |
| spellingShingle | Carmela Vitanza Pietro Zamboni Necessary and sufficient conditions for Hölder continuity of solutions of degenerate Schrödinger operators Le Matematiche |
| title | Necessary and sufficient conditions for Hölder continuity of solutions of degenerate Schrödinger operators |
| title_full | Necessary and sufficient conditions for Hölder continuity of solutions of degenerate Schrödinger operators |
| title_fullStr | Necessary and sufficient conditions for Hölder continuity of solutions of degenerate Schrödinger operators |
| title_full_unstemmed | Necessary and sufficient conditions for Hölder continuity of solutions of degenerate Schrödinger operators |
| title_short | Necessary and sufficient conditions for Hölder continuity of solutions of degenerate Schrödinger operators |
| title_sort | necessary and sufficient conditions for holder continuity of solutions of degenerate schrodinger operators |
| url | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/418 |
| work_keys_str_mv | AT carmelavitanza necessaryandsufficientconditionsforholdercontinuityofsolutionsofdegenerateschrodingeroperators AT pietrozamboni necessaryandsufficientconditionsforholdercontinuityofsolutionsofdegenerateschrodingeroperators |