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

Title & Authors
Lq(Lp) -THEORY OF PARABOLIC PDEs WITH VARIABLE COEFFICIENTS
Kim, Kyeong-Hun;

Abstract
Second-order parabolic equations with variable coefficients are considered on $\small{\mathbb{R}^d}$ and $\small{C^1}$ domains. Existence and uniqueness results are given in $\small{L_q(L_p)}$-spaces, where it is allowed for the powers of summability with respect to space and time variables to be different.
Keywords
parabolic equations$\small{L_q(L_p)}$-theory;Sobolev spaces with weights;
Language
English
Cited by
1.
Finite Difference Schemes for Stochastic Partial Differential Equations in Sobolev Spaces, Applied Mathematics & Optimization, 2015, 72, 1, 77
2.
On the solvability of degenerate stochastic partial differential equations in Sobolev spaces, Stochastic Partial Differential Equations: Analysis and Computations, 2015, 3, 1, 52
3.
Stochastic regularization effects of semi-martingales on random functions, Journal de Mathématiques Pures et Appliquées, 2016, 106, 6, 1141
References
1.
A. Benedek, A. P. Calderon, and R. Panzone, Convolution operators on Banach space valued functions, Proc. Nat. Acad. Sci. U.S.A. 48 (1962), 356-365

2.
K. Kim and N. V. Krylov, On the Sobolev space theory of parabolic and elliptic equations in \$C^1\$ domains, SIAM J. Math. Anal. 36 (2004), no. 2, 618-642

3.
N. V. Krylov, Some properties of traces for stochastic and deterministic parabolic weighted Sobolev spaces, J. Funct. Anal. 183 (2001), no. 1, 1-41

4.
N. V. Krylov, The heat equation in \$L_q((0,T),L_p)\$-spaces with weights, SIAM J. Math. Anal. 32 (2001), no. 5, 1117-1141

5.
N. V. Krylov, An Analytic Approach to SPDEs, Stochastic partial differential equations: six perspectives, 185-242, Math. Surveys Monogr., 64, Amer. Math. Soc., Providence, RI, 1999

6.
N. V. Krylov, Weighted Sobolev spaces and Laplace's equation and the heat equations in a half space, Comm. Partial Differential Equations 24 (1999), no. 9-10, 1611-1653

7.
N. V. Krylov, Some properties of weighted Sobolev spaces in \$R^d_+\$, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 (1999), no. 4, 675-693

8.
S. V. Lototksy, Dirichlet problem for stochastic parabolic equations in smooth domains, Stochastics and Stochastics Rep. 68 (1999), no. 1-2, 145-175

9.
S. V. Lototksy, Sobolev spaces with weights in domains and boundary value problems for degenerate elliptic equations, Methods Appl. Anal. 7 (2000), no. 1, 195-204

10.
P. Weidemaier, On the sharp initial trace of functions with derivatives in \$L_q(0,T;L_p(\Omega))\$, Boll. Un. Mat. Ital. B (7) 9 (1995), no. 2, 321-338