Abstract
We establish global Gaussian estimates for the Green's matrix of divergence form, second order parabolic systems in a cylindrical domain under the assumption that weak solutions of the system vanishing on a portion of the boundary satisfy a certain local boundedness estimate and a local Hölder estimate. From these estimates, we also derive global estimates for the Green's matrix for elliptic systems with bounded measurable coefficients in two dimensional domains. We present a unified approach valid for both the scalar and vectorial cases and discuss several applications of our result.
| Original language | English |
|---|---|
| Pages (from-to) | 339-372 |
| Number of pages | 34 |
| Journal | Potential Analysis |
| Volume | 36 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2012 Feb |
Bibliographical note
Funding Information:Acknowledgements Sungwon Cho was supported by the National Research Foundation of Korea Grant funded by the Korean Government (Ministry of Education, Science and Technology)[NRF-2010-359-C00003]. Hongjie Dong was partially supported by the National Science Foundation under agreement No. DMS-0800129. Seick Kim was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology (2010-0008224) and also WCU(World Class University) program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology (R31-2008-000-10049-0).
All Science Journal Classification (ASJC) codes
- Analysis