## Regularity theory and traces of $\mathcal {A}$-harmonic functions

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- by Pekka Koskela, Juan J. Manfredi and Enrique Villamor PDF
- Trans. Amer. Math. Soc.
**348**(1996), 755-766 Request permission

## Abstract:

In this paper we discuss two different topics concerning $\mathcal {A}$- harmonic functions. These are weak solutions of the partial differential equation \begin{equation*}\text {div}(\mathcal {A}(x,\nabla u))=0,\end{equation*} where $\alpha (x)|\xi |^{p-1}\le \langle \mathcal {A}(x,\xi ),\xi \rangle \le \beta (x) |\xi |^{p-1}$ for some fixed $p\in (1,\infty )$, the function $\beta$ is bounded and $\alpha (x)>0$ for a.e. $x$. First, we present a new approach to the regularity of $\mathcal {A}$-harmonic functions for $p>n-1$. Secondly, we establish results on the existence of nontangential limits for $\mathcal {A}$-harmonic functions in the Sobolev space $W^{1,q}(\mathbb {B})$, for some $q>1$, where $\mathbb {B}$ is the unit ball in $\mathbb {R}^n$. Here $q$ is allowed to be different from $p$.## References

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## Additional Information

**Pekka Koskela**- Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
- MR Author ID: 289254
- Email: pkoskela@math.jyu.fi
**Juan J. Manfredi**- Affiliation: Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
- MR Author ID: 205679
- Email: manfredit@pitt.edu
**Enrique Villamor**- Affiliation: Department of Mathematics, Florida International University, Miami, Florida 33199
- Email: villamor@fiu.edu
- Received by editor(s): June 7, 1994
- Received by editor(s) in revised form: January 23, 1995
- Additional Notes: Research of the first author was partially supported by the Academy of Finland and NSF grant DMS-9305742

Research of the second author was partially supported by NSF grant DMS-9101864 - © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**348**(1996), 755-766 - MSC (1991): Primary 35B65; Secondary 31B25
- DOI: https://doi.org/10.1090/S0002-9947-96-01430-4
- MathSciNet review: 1311911