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

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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.

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Authors and Affiliations

  1. Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, 310032, China

    Yong-yang Jin

  2. Zhejiang Vocational College of Commerce, Hangzhou, 310014, China

    Jie-lin Lü

  3. Department of Mathematics, Taizhou University, Linhai, 317000, China

    Rong-fei Lin

Authors
  1. Yong-yang Jin
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  2. Jie-lin Lü
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  3. Rong-fei Lin
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Corresponding author

Correspondence to Yong-yang Jin.

Additional information

Supported by Natural Science Foundation of Zhejiang Province (No.Y60900359, Y6090383), Department of Education of Zhejiang Province (No.Z200803357).

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Jin, Yy., Lü, Jl. & Lin, Rf. Hölder continuity for a class of strongly degenerate Schrödinger operator formed by vector fields. Acta Math. Appl. Sin. Engl. Ser. 29, 281–288 (2013). https://doi.org/10.1007/s10255-011-0098-2

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  • DOI: https://doi.org/10.1007/s10255-011-0098-2

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