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The Dirichlet problem for non-divergence parabolic equations with discontinuous in time coefficients in a wedge
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
St.-Petersburg Department of Steklov Institute, St.-Petersburg, Russia; St Petersburg State University, Russia .
2014 (English)In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 287, no 10, 1142-1165 p.Article in journal (Refereed) Published
Abstract [en]

We consider the Dirichlet problem in a wedge for parabolic equation whose coefficients are measurable function of t. We obtain coercive estimates in weighted L-p,L-q-spaces. The concept of "critical exponent" introduced in the paper plays here the crucial role. Various important properties of the critical exponent are proved. We give applications to the Dirichlet problem for linear and quasi-linear non-divergence parabolic equations with discontinuous in time coefficients in cylinders Omega x (0, T), where Omega is a bounded domain with an edge or with a conical point.

Place, publisher, year, edition, pages
Wiley-VCH Verlagsgesellschaft, 2014. Vol. 287, no 10, 1142-1165 p.
Keyword [en]
Non-divergence parabolic equations; discontinuous in time coefficients; Dirichlet problem; coercive estimates in a wedge; anisotropic Sobolev spaces
National Category
URN: urn:nbn:se:liu:diva-109392DOI: 10.1002/mana.201100352ISI: 000339011500005OAI: diva2:738027
Available from: 2014-08-15 Created: 2014-08-15 Last updated: 2014-09-18Bibliographically approved

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Kozlov, Vladimir
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Mathematics and Applied MathematicsThe Institute of Technology
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ReferencesLink to record
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