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A regularity theory for quasi-linear Stochastic PDEs in weighted Sobolev spaces
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9초록
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.
키워드
Nonlinear stochastic partial differential equations; Equations of divergence type; Weighted Sobolev space; PARTIAL-DIFFERENTIAL-EQUATIONS; DOMAINS; SPDES
- 제목
- A regularity theory for quasi-linear Stochastic PDEs in weighted Sobolev spaces
- 저자
- Kim, Ildoo; Kim, Kyeong-Hun
- 발행일
- 2018-02
- 유형
- Article
- 권
- 128
- 호
- 2
- 페이지
- 622 ~ 643