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The Oblique Derivative Problem for a Nonuniformly Parabolic Equation

The Oblique Derivative Problem for a Nonuniformly Parabolic Equation Di erential Equations, Vol. 37, No. 12, 2001, pp. 1720{1730. Translated from Di erentsial'nye Uravneniya, Vol. 37, No. 12, 2001, pp. 1637{1645. Original Russian Text Copyright c 2001 by Pukal'skii. PARTIAL DIFFERENTIAL EQUATIONS The Oblique Derivative Problem for a Nonuniformly Parabolic Equation I. D. Pukal'skii Chernovtsy State University, Chernovtsy, Ukraine Received March 5, 1999 The general nonhomogeneous parabolic boundary value problem with coecients discontinuous on a hyperplane and the oblique derivative problem for parabolic equations with minimal smooth- ness and a speci c degeneration in the coecients were solved in [1, 2]. In the present paper, using the maximum principle and apriori estimates, we analyze the oblique derivative problem for a second-order nonuniformly parabolic equation without restrictions on the order of power-law degeneration of the coecients but with a sign inequality for the coecient of the zero-order derivative. STATEMENT OF THE PROBLEM AND THE MAIN RESULT Let D be a bounded convex domain in R with boundary @D. In the domain Q =(0;T ) D, we consider the boundary value problem " # n n X X 1 1 1 1 Lu = D A (t;x)D D A (t;x)D A (t;x) u(t;x)= f (t;x); (1) ij http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

The Oblique Derivative Problem for a Nonuniformly Parabolic Equation

Pukal'skii, I.
Differential Equations , Volume 37 (12) – Oct 9, 2004
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Publisher
Springer Journals
Copyright
Copyright © 2001 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/A:1014467207063
Publisher site
See Article on Publisher Site

Abstract

Di erential Equations, Vol. 37, No. 12, 2001, pp. 1720{1730. Translated from Di erentsial'nye Uravneniya, Vol. 37, No. 12, 2001, pp. 1637{1645. Original Russian Text Copyright c 2001 by Pukal'skii. PARTIAL DIFFERENTIAL EQUATIONS The Oblique Derivative Problem for a Nonuniformly Parabolic Equation I. D. Pukal'skii Chernovtsy State University, Chernovtsy, Ukraine Received March 5, 1999 The general nonhomogeneous parabolic boundary value problem with coecients discontinuous on a hyperplane and the oblique derivative problem for parabolic equations with minimal smooth- ness and a speci c degeneration in the coecients were solved in [1, 2]. In the present paper, using the maximum principle and apriori estimates, we analyze the oblique derivative problem for a second-order nonuniformly parabolic equation without restrictions on the order of power-law degeneration of the coecients but with a sign inequality for the coecient of the zero-order derivative. STATEMENT OF THE PROBLEM AND THE MAIN RESULT Let D be a bounded convex domain in R with boundary @D. In the domain Q =(0;T ) D, we consider the boundary value problem " # n n X X 1 1 1 1 Lu = D A (t;x)D D A (t;x)D A (t;x) u(t;x)= f (t;x); (1) ij

Journal

Differential Equations – Springer Journals

Published: Oct 9, 2004

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