## Differential and Integral Equations

### A Wiener estimate for relaxed Dirichlet problems in dimension $N\geq 2$

#### Abstract

We prove a Wiener energy estimate for relaxed Dirichlet problems $Lu + \mu u =\nu$ in $\Omega$, with $L$ a uniformly elliptic operator with bounded coefficients, $\mu$ a measure of $\mathcal {M}_0(\Omega)$, $\nu$ a Kato measure and $\Omega$ a bounded open set of $\mathbb{R}^N$, $N \geq 2$. Choosing a particular $\mu$, we obtain an energy estimate also for classical variational Dirichlet problems.

#### Article information

Source
Differential Integral Equations, Volume 8, Number 4 (1995), 849-866.

Dates
First available in Project Euclid: 20 May 2013

https://projecteuclid.org/euclid.die/1369055614

Mathematical Reviews number (MathSciNet)
MR1306595

Zentralblatt MATH identifier
0815.35013

Subjects
Primary: 35J25: Boundary value problems for second-order elliptic equations
Secondary: 35B45: A priori estimates

#### Citation

Garroni, Adriana. A Wiener estimate for relaxed Dirichlet problems in dimension $N\geq 2$. Differential Integral Equations 8 (1995), no. 4, 849--866. https://projecteuclid.org/euclid.die/1369055614