IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v130y2020i1p1-19.html
   My bibliography  Save this article

W2,p-solutions of parabolic SPDEs in general domains

Author

Listed:
  • Du, Kai

Abstract

The Dirichlet problem for a class of stochastic partial differential equations is studied in Sobolev spaces. The existence and uniqueness result is proved under certain compatibility conditions that ensure the finiteness of Lp(Ω×(0,T),W2,p(G))-norms of solutions. The Hölder continuity of solutions and their derivatives is also obtained by embedding.

Suggested Citation

  • Du, Kai, 2020. "W2,p-solutions of parabolic SPDEs in general domains," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 1-19.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:1:p:1-19
    DOI: 10.1016/j.spa.2018.12.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414918301509
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2018.12.015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gerencsér, Máté & Gyöngy, István, 2019. "A Feynman–Kac formula for stochastic Dirichlet problems," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 995-1012.
    2. Kyeong-Hun Kim, 2014. "A Weighted Sobolev Space Theory of Parabolic Stochastic PDEs on Non-smooth Domains," Journal of Theoretical Probability, Springer, vol. 27(1), pages 107-136, March.
    3. Tongkeun Chang & Kijung Lee & Minsuk Yang, 2013. "On Initial-Boundary Value Problem of the Stochastic Heat Equation in Lipschitz Cylinders," Journal of Theoretical Probability, Springer, vol. 26(4), pages 1135-1164, December.
    4. Kyeong-Hun Kim, 2008. "L p -Theory of Parabolic SPDEs Degenerating on the Boundary of C 1 Domains," Journal of Theoretical Probability, Springer, vol. 21(1), pages 169-192, March.
    5. 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.
    6. Krylov, N.V., 2009. "On divergence form SPDEs with VMO coefficients in a half space," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 2095-2117, June.
    7. Kim, Kyeong-Hun, 2009. "Sobolev space theory of SPDEs with continuous or measurable leading coefficients," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 16-44, January.
    8. Kim, Kyeong-Hun & Lee, Kijung, 2013. "A note on Wpγ-theory of linear stochastic parabolic partial differential systems," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 76-90.
    9. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:130:y:2020:i:1:p:1-19. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.