# Hölder continuity for a class of strongly degenerate Schrödinger operator formed by vector fields

Hölder continuity for a class of strongly degenerate Schrödinger operator formed by vector fields In this paper we obtain the Hölder continuity property of the solutions for a class of degenerate Schrödinger equation generated by the vector fields: $$- \sum\limits_{i,j = 1}^m {X_j^* \left( {a_{ij} \left( x \right)X_i u} \right) + \vec bXu + vu = 0,}$$ where X = {X 1, ...,X m } is a family of C ∞ vector fields satisfying the Hörmander condition, and the lower order terms belong to an appropriate Morrey type space. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# Hölder continuity for a class of strongly degenerate Schrödinger operator formed by vector fields

, Volume 29 (2) – Apr 10, 2013
8 pages

/lp/springer-journals/h-lder-continuity-for-a-class-of-strongly-degenerate-schr-dinger-F5qmqVr32r
Publisher
Springer Journals
Copyright © 2013 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-011-0098-2
Publisher site
See Article on Publisher Site

### Abstract

In this paper we obtain the Hölder continuity property of the solutions for a class of degenerate Schrödinger equation generated by the vector fields: $$- \sum\limits_{i,j = 1}^m {X_j^* \left( {a_{ij} \left( x \right)X_i u} \right) + \vec bXu + vu = 0,}$$ where X = {X 1, ...,X m } is a family of C ∞ vector fields satisfying the Hörmander condition, and the lower order terms belong to an appropriate Morrey type space.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Apr 10, 2013

### References

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