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A regularity theory for quasi-linear Stochastic PDEs in weighted Sobolev spaces
- Authors
- Kim, Ildoo; Kim, Kyeong-Hun
- Issue Date
- 2월-2018
- Publisher
- ELSEVIER SCIENCE BV
- Keywords
- Nonlinear stochastic partial differential equations; Equations of divergence type; Weighted Sobolev space
- Citation
- STOCHASTIC PROCESSES AND THEIR APPLICATIONS, v.128, no.2, pp.622 - 643
- Indexed
- SCIE
SCOPUS
- Journal Title
- STOCHASTIC PROCESSES AND THEIR APPLICATIONS
- Volume
- 128
- Number
- 2
- Start Page
- 622
- End Page
- 643
- ISSN
- 0304-4149
- Abstract
- We study the second-order quasi-linear stochastic partial differential equations (SPDEs) defined on C-1-domains. The coefficients are random functions depending on t, x and the unknown solutions. We prove the uniqueness and existence of solutions in appropriate Sobolev spaces, and in addition, we obtain L-p and Holder estimates of both the solution and its gradient. (C) 2017 Elsevier B.V. All rights reserved.
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