We study the second-order quasi-linear stochastic partial differential equations (SPDEs) defined on C1-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 Lp and Hölder estimates of both the solution and its gradient.
Bibliographical noteFunding Information:
The research of the first author was supported by the TJ Park Science Fellowship of POSCO TJ Park Foundation . The research of the second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 20120005158 ).
© 2017 Elsevier B.V.
- Equations of divergence type
- Nonlinear stochastic partial differential equations
- Weighted Sobolev space
ASJC Scopus subject areas
- Statistics and Probability
- Modelling and Simulation
- Applied Mathematics