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 |
| Summary: | 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. |
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| ISSN: | 0373-3505 2037-5298 |