# Tagged Questions

**4**

votes

**1**answer

144 views

### variation of the obstacle in the obstacle problem

Suppose $D \subset \Bbb C$ with smooth boundary. Let $f \in C^{1,1}(D)$. Let $\varphi$ be the supremum of all members in the set
$$\lbrace g \in C^{\infty}(\overline{D})| g \ is \ subharmonic \ and ...

**1**

vote

**1**answer

305 views

### Almost analytic continuation

Let $f\in S^{\alpha}$ for some $\alpha \in \mathbb{R}$(which means that f is smooth and satisfies $|D^{\beta}f|\leq C(1+|x|)^{\alpha-\beta}$),a function $\tilde{f}$ on $\mathbb{C}$ is called an almost ...

**7**

votes

**2**answers

709 views

### Characterize where the Dirichlet Problem for the Laplacian is always solvable

Conway's 1978 textbook Functions of One Complex Variable I gives an unsatisfying characterization of the regions for which the Dirichlet Problem can always be solved, and then comments no cleaner ...

**4**

votes

**0**answers

764 views

### A “Cauchy integral formula” for the Poisson kernel?

The inspiration for this question is in a certain breakdown of the analogy between holomorphic and harmonic functions.
First recall the Cauchy integral formula:
Let $U$ be an open subset of ...

**2**

votes

**0**answers

217 views

### Finer properties of a sequence of harmonic functions

This was a question that arose for me when I was thinking about how one proves strong unique continuation for elliptic equations. I never could come up with a satisfactory answer.
Background:
When ...

**2**

votes

**1**answer

844 views

### The normal derivative of the Green's function

I was wondering if anything was known about the following:
Let $\mathbb{D}^2=\lbrace x^2+y^2< 1 \rbrace \subset \mathbb{R}^2$ be the open unit disk.
Consider now the Green's functions $G(z; p)$ ...