TY - JOUR
T1 - A regularity theory for quasi-linear Stochastic PDEs in weighted Sobolev spaces
AU - Kim, Ildoo
AU - Kim, Kyeong Hun
N1 - Funding 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 ).
Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2018/2
Y1 - 2018/2
N2 - 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.
AB - 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.
KW - Equations of divergence type
KW - Nonlinear stochastic partial differential equations
KW - Weighted Sobolev space
UR - http://www.scopus.com/inward/record.url?scp=85023625298&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2017.06.006
DO - 10.1016/j.spa.2017.06.006
M3 - Article
AN - SCOPUS:85023625298
VL - 128
SP - 622
EP - 643
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
IS - 2
ER -