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Lq(Lp) theory and Hölder estimates for parabolic SPDEs

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  • Kim, Kyeong-Hun

Abstract

Hölder estimates are given for the solutions of parabolic stochastic partial differential equations in C1 domains. Also existence and uniqueness theorems are presented in Lp-spaces with weights. It is allowed that the powers of summability with respect to space and time to be different.

Suggested Citation

  • Kim, Kyeong-Hun, 2004. "Lq(Lp) theory and Hölder estimates for parabolic SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 114(2), pages 313-330, December.
    • Handle: RePEc:eee:spapps:v:114:y:2004:i:2:p:313-330
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    References listed on IDEAS

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    1. Kim, Kyeong-Hun, 2004. "On stochastic partial differential equations with variable coefficients in C1 domains," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 261-283, August.
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    Cited by:

    1. Kim, Kyeong-Hun, 2014. "A Sobolev space theory for parabolic stochastic PDEs driven by Lévy processes on C1-domains," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 440-474.
    2. Kim, Ildoo & Kim, Kyeong-Hun, 2018. "A regularity theory for quasi-linear Stochastic PDEs in weighted Sobolev spaces," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 622-643.

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