Differential and Integral Equations

Comparison results for a linear elliptic equation with mixed boundary conditions

B. Brandolini, M. R. Posteraro, and R. Volpicelli

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In this paper we study a linear elliptic equation having mixed boundary conditions, defined in a connected open set $\Omega $ of $\mathbb{R}^{n}$. We prove a comparison result with a suitable ``symmetrized'' Dirichlet problem which cannot be uniformly elliptic depending on the regularity of $ \partial \Omega $. Regularity results for non-uniformly elliptic equations are also given.

Article information

Differential Integral Equations, Volume 16, Number 5 (2003), 625-639.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J25: Boundary value problems for second-order elliptic equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35B65: Smoothness and regularity of solutions 35J70: Degenerate elliptic equations


Brandolini, B.; Posteraro, M. R.; Volpicelli, R. Comparison results for a linear elliptic equation with mixed boundary conditions. Differential Integral Equations 16 (2003), no. 5, 625--639. https://projecteuclid.org/euclid.die/1356060631

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