$L_p$-Estimates for SPDE with Discontinuous Coefficients in Domains

Kyeong-Hun Kim (University of Utah)

Abstract


Stochastic partial differential equations of divergence form with discontinuous and unbounded coefficients are considered in $C^1$ domains. Existence and uniqueness results are given in weighted $L_p$ spaces, and Holder type estimates are presented.

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Pages: 1-20

Publication Date: February 11, 2005

DOI: 10.1214/EJP.v10-234

References

    [1] K. Kim, On stochastic partial differential equations with variable coefficients in C^1 domains, Stochastic processes and their applications,  V.112 (2004), 261-283. Math. Review MR2073414

    [2] K. Kim, On Lp-theory of SPDEs of divergence form in C^1 domains, Probability theory and related fields, V.130(4) (2004), 473-492. Math. Review  MR2102888

    [3] K. Kim, Lq(Lp) theory and H"older estimates for parabolic SPDE, Stochastic processes and their applications, V.114 (2004), 313-330. Math. Review MR2101247

    4] K. Kim and N.V. Krylov, On SPDEs with variable coefficients in one space dimension, Potential Anal, V.21(3) (2004), 203-239.
         Math. Review MR2075669
    [5] K. Kim and N.V. Krylov, On the Sobolev space theory of parabolic and elliptic equations in C^1 domains, SIAM J. Math. Anal, V.36(2) (2004), 618-642.

    [6] N.V. Krylov, SPDEs in Lq((0,tau],Lp)  spaces , Electronic Journal of Probability, V.5(13) (2000), 1-29.
          Math Review  MR1781025 (2001g:60156)
    [7] N.V. Krylov, An analytic approach to SPDEs, Stochastic Partial Differential Equations: Six Perspectives, Mathematical Surveys and   Monographs, V.64, AMS, Providence, RI, 1999. Math. Review MR1661766 (99j: 60093)

    [8] N.V. Krylov, Weighted Sobolev spaces and Laplace equations and the heat equations in a half space , Comm. in PDEs, V.23(9-10) (1999), 1611-1653. Math. Review  MR1708104 (2000j:46065)

    [9] N.V. Krylov, Lectures on elliptic and parabolic equations in H"older space , American Mathematical Society, Graduate Studies in Mathematics, V.12, Providence, RI, 1996. Math Review MR1406091 (97i:35001)

    [10] N.V. Krylov and S.V. Lototsky, A Sobolev space theory of SPDEs with constant coefficients in a half line, SIAM J. on Math Anal., V.30(2) (1998), 298-325. Math Review MR1664761 (99k:60164)

    [11] N.V. Krylov and S.V. Lototsky, A Sobolev space theory of SPDEs with constant coefficients in a half space, SIAM J. on Math Anal., V.31(1) (1999), 19-33. Math Review MR1720129 (2001a:60072)

    [12] S.V. Lototsky, Sobolev spaces with weights in domains and boundary value problems for degenerate elliptic equations, Methods and Applications of Analysis, V.7(1) (2000), 195-204. Math Review  MR1742721 (2000i:60069)

    [13] G. Pulvirenti, Sulla sommabilit`a Lp delle derivate prime delle soluzioni deboli del problema di Cauchy-Dirichlet per le equazioni lineari del secondo ordine di tipo parabolico, Le Matematiche, V.22 (1967), 250-265. Math Review MR0228842 (37 #4421)

    [14] B.L. Rozovskii, Stochastic evolution systems, Kluwer, Dordrecht, 1990. Math Review  MR1135324 (92k:60136)

    [15] H. Yoo, Lp-estimate for stochastic PDEs with discontinuous coefficients , Stochastic Anal. Appl., V.17(4) (999), 678-711.
           Math Review  MR1693563 (2000f:60093)
    [16] H.Yoo, On the unique solvability of some nonlinear stochastic PDEs , Electronic Journal of Probability, V.3(11) (1998), 1-22.
           Math Review  MR1639464 (99h:60126)
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