# Tagged Questions

**3**

votes

**1**answer

263 views

### on an inequality of Brezis-Lieb

In their 1983 JFA paper Brezis and Lieb have shown, among many other things, a PoincarĂ©-type inequality: in the case of a harmonic function $f$ on a bounded domain $\Omega$, their inequality ((3.14) ...

**6**

votes

**2**answers

440 views

### Boundary regularity for the Dirichlet problem

Let us consider the unit ball $B^n$ of $\mathbf{R}^n$ and $K = B^{n-1}(0,1/2) \times \{0\}$ the ball of dimension $n-1$ and radius $1/2$ lying on the equator.
We wish to solve the Dirichlet problem ...