# Tagged Questions

**5**

votes

**0**answers

101 views

### Reference Request: Elliptic differential operators in the Fréchet setting

Normally the theory of (elliptic) differential operators between vector bundles (or $\mathbb{R}^n$) is presented in the language of Sobolev spaces. I'm searching for a book (or something similar) ...

**3**

votes

**1**answer

167 views

### Caccioppoli-Leray Inequality for De Giorgi's theorem proof

I am studying De Giorgi's proof of Holder continuity of solutions of elliptic equations with bounded measurable coefficients.
This is the translation of the original paper
De Giorgi paper
At page ...

**0**

votes

**2**answers

505 views

### Interior regularity for elliptic equations

The monograph "Non-Homogeneous Boundary Value Problems and Applications" by Lions and Magenes is infamous for developing a truly extensive regularity theory for elliptic problems on domains, and for ...

**1**

vote

**1**answer

213 views

### Boundary Value Problem in the space of Distributions

I will not be rigirous cause my question does not require this. It is well known how to treat the solution (for example) of the problem $\Delta u=f$ in $\Omega$ and $u=g$ on $\partial \Omega$ by the ...

**1**

vote

**2**answers

373 views

### Smooth Sobolev extension from $W^{1,p}(U)$ to $W^{1,p} (\mathbb{R}^n) $

The question I would be asking is roughly : do the smooth Sobolev functions defined on an open bounded domain extend to smooth Sobolev functions on the Euclidean space ?
For detail :
Fix $p \geq 1. ...

**1**

vote

**3**answers

445 views

### Finding an $H^1$ function given its values on $\partial\Omega$

Background
I've met this problem when I was trying to convert a elliptic PDE problem
into the corresponding variational problem in order to apply finite element method.
The PDE is an elliptic PDE ...