TY - JOUR
T1 - On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains
AU - Dong, Hongjie
AU - Krylov, N. V.
AU - Li, Xu
PY - 2013
Y1 - 2013
N2 - The solvability in the Sobolev spaces W1,2p, p > d +1, of the terminalboundary value problem is proved for a class of fully nonlinear parabolic equations, including parabolic Bellman's equations, in bounded cylindrical domains, in the case of VMO " coefficients" . The solvability in W2p, p > d, of the corresponding elliptic boundary-value problem is also obtained.
AB - The solvability in the Sobolev spaces W1,2p, p > d +1, of the terminalboundary value problem is proved for a class of fully nonlinear parabolic equations, including parabolic Bellman's equations, in bounded cylindrical domains, in the case of VMO " coefficients" . The solvability in W2p, p > d, of the corresponding elliptic boundary-value problem is also obtained.
KW - Bellman's equations
KW - Fully nonlinear elliptic and parabolic equations
KW - Vanishing mean oscillation
UR - http://www.scopus.com/inward/record.url?scp=84871490924&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84871490924&partnerID=8YFLogxK
U2 - 10.1090/S1061-0022-2012-01231-8
DO - 10.1090/S1061-0022-2012-01231-8
M3 - Article
AN - SCOPUS:84871490924
SN - 1061-0022
VL - 24
SP - 39
EP - 69
JO - St. Petersburg Mathematical Journal
JF - St. Petersburg Mathematical Journal
IS - 1
ER -