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The Dirichlet problem for non‐divergence parabolic equations with discontinuous in time coefficients in a wedge
Author(s) -
Kozlov Vladimir,
Nazarov Alexander
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201100352
Subject(s) - mathematics , mathematical analysis , wedge (geometry) , bounded function , dirichlet problem , exponent , conical surface , divergence (linguistics) , parabolic partial differential equation , dirichlet distribution , critical exponent , domain (mathematical analysis) , nonlinear system , partial differential equation , geometry , boundary value problem , linguistics , philosophy , physics , quantum mechanics , scaling
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 , 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 Ω × ( 0 , T ) , where Ω is a bounded domain with an edge or with a conical point.