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1997 The Dirichlet problem for a class of ultraparabolic equations
Maria Manfredini
Adv. Differential Equations 2(5): 831-866 (1997).

Abstract

In this paper we study the Dirichlet problem for a class of ultraparabolic equations. More precisely, we prove the existence of a generalized Perron-Wiener solution and we provide a geometric condition for the regularity of the boundary points which extends the classical Zaremba exterior cone criterion to our setting. The main steps for deriving our results are: i) the introduction in $\mathbf{R}^{N+1}$ of a homogeneous structure; ii) the proof of some interior estimates in a suitable space of Hölder-continuous functions; iii) the construction of a basis of open subsets of $\mathbf{R}^{N+1}$ for which the Dirichlet problem is univocally solvable.

Citation

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Maria Manfredini. "The Dirichlet problem for a class of ultraparabolic equations." Adv. Differential Equations 2 (5) 831 - 866, 1997.

Information

Published: 1997
First available in Project Euclid: 22 April 2013

zbMATH: 1023.35518
MathSciNet: MR1751429

Subjects:
Primary: 35G15, 35K22, 35K70

Rights: Copyright © 1997 Khayyam Publishing, Inc.

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Vol.2 • No. 5 • 1997
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