Lq(Lp)-THEORY OF PARABOLIC PDEs WITH VARIABLE COEFFICIENTS

다국어 초록 (Multilingual Abstract)

Second-order parabolic equations with variable coecientsare considered on Rd and C¹ domains. Existence and uniqueness resultsare given in Lq(Lp)-spaces, where it is allowed for the powers of summa-bility with respect to space and time variables to be dierent.

참고문헌 (Reference)

1 N. V. Krylov, "Weighted Sobolev spaces and Laplace’ equation and the heat equations in a half space" 24 (24): 1611-1653, 1999

2 N. V. Krylov, "The heat equation in Lq((0 T)Lp)-spaces with weights" 32 (32): 1117-1141, 2001

3 N. V. Krylov, "Some properties of weighted Sobolev spaces in Rd + , Ann. Scuola Norm" 28 (28): 675-693, 1999

4 N. V. Krylov, "Some properties of traces for stochastic and deterministic parabolic weighted Sobolev spaces" 183 (183): 1-41, 2001

5 S. V. Lototksy, "Sobolev spaces with weights in domains and boundary value problems for degenerate elliptic equations" 7 (7): 195-204, 2000

6 P.Weidemaier, "On the sharp initial trace of functions with derivatives in Lq(0 TLp(Ω))" 9 (9): 321-338, 1995

7 K. Kim, "On the Sobolev space theory of parabolic and elliptic equa-tions in C1 domains" 36 (36): 618-642, 2004

8 S. V. Lototksy, "Dirichlet problem for stochastic parabolic equations in smooth domains" 68 (68): 145-175, 1999

9 A. Benedek, "Convolution operators on Banach space valued functions" 48 : 356-365, 1962

10 N. V. Krylov, "An Analytic Approach to SPDEs, Stochastic partial differential equations: six perspectives" Amer. Math. Soc. 185-242, 1999