## Advances in Differential Equations

- Adv. Differential Equations
- Volume 6, Number 7 (2001), 873-895.

### Nonlinear elliptic problems with $p$-structure under mixed boundary value conditions in polyhedral domains

#### Abstract

Nonlinear elliptic systems with $p$-structure for $p \! \geq \! 2$, such as \[ -\mbox{div}\left((1+|\nabla u|^{p-2})\nabla u\right) =f(x)+\sum_{i=1}^n\partial_if_i(x) ,\] are considered under mixed boundary value conditions on nonsmooth domains. Regularity results in fractional-order Sobolev spaces are proven, e.g., $u\in W^{r,p}(\Omega)$ for all $r <1+\frac{1}{p}$ and $|\nabla u|^p\in W^{s,1}(\Omega)$ for some $s>1$.

#### Article information

**Source**

Adv. Differential Equations Volume 6, Number 7 (2001), 873-895.

**Dates**

First available in Project Euclid: 2 January 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1357140567

**Mathematical Reviews number (MathSciNet)**

MR1829000

**Zentralblatt MATH identifier**

1223.35150

**Subjects**

Primary: 35J55

Secondary: 35J25: Boundary value problems for second-order elliptic equations 35J60: Nonlinear elliptic equations 35J65: Nonlinear boundary value problems for linear elliptic equations

#### Citation

Ebmeyer, Carsten. Nonlinear elliptic problems with $p$-structure under mixed boundary value conditions in polyhedral domains. Adv. Differential Equations 6 (2001), no. 7, 873--895. https://projecteuclid.org/euclid.ade/1357140567