The Dirichlet problem for non‐divergence parabolic equations with discontinuous in time coefficients in a wedge

Vladimir Kozlov; Alexander Il'ich Nazarov

doi:10.1002/mana.201100352

journal article Mar 18, 2014

The Dirichlet problem for non‐divergence parabolic equations with discontinuous in time coefficients in a wedge

Vladimir Kozlov Alexander Il'ich Nazarov

Mathematische Nachrichten Vol. 287 No. 10 pp. 1142-1165 · Wiley

View at Publisher Save 10.1002/mana.201100352

Abstract

We consider the Dirichlet problem in a wedge for parabolic equation whose coefficients are measurable function of t. We obtain coercive estimates in weighted ‐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 , where Ω is a bounded domain with an edge or with a conical point.

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Vladimir Kozlov, Alexander Il'ich Nazarov

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Metrics

17

Citations

18

References

Details

Published: Mar 18, 2014
Vol/Issue: 287(10)
Pages: 1142-1165
License: View

Authors

V

Vladimir Kozlov

Department of Mathematics Linköping University S‐581 83 Linköping Sweden

A

Alexander Il'ich Nazarov

St.‐Petersburg Department of Steklov Institute St.‐Petersburg 191023 Russia; Mathematics and Mechanics Department St.‐Petersburg State University St.‐Petersburg 198504 Russia

Funding

St. Petersburg University Award: 6.38.670.2013

RFBR Award: 12-01-00439

Cite This Article

Vladimir Kozlov, Alexander Il'ich Nazarov (2014). The Dirichlet problem for non‐divergence parabolic equations with discontinuous in time coefficients in a wedge. Mathematische Nachrichten, 287(10), 1142-1165. https://doi.org/10.1002/mana.201100352

The Dirichlet problem for non‐divergence parabolic equations with discontinuous in time coefficients in a wedge

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