Advances in Differential Equations

The Dirichlet problem for a class of ultraparabolic equations

Maria Manfredini

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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.

Article information

Adv. Differential Equations, Volume 2, Number 5 (1997), 831-866.

First available in Project Euclid: 22 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K70: Ultraparabolic equations, pseudoparabolic equations, etc. 35K22 35G15: Boundary value problems for linear higher-order equations


Manfredini, Maria. The Dirichlet problem for a class of ultraparabolic equations. Adv. Differential Equations 2 (1997), no. 5, 831--866.

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