Regularity theory and traces

of -harmonic functions

Authors:
Pekka Koskela, Juan J. Manfredi and Enrique Villamor

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

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we discuss two different topics concerning -

harmonic functions. These are weak solutions of the partial differential equation

where for some fixed , the function is bounded and for a.e. . First, we present a new approach to the regularity of -harmonic functions for . Secondly, we establish results on the existence of nontangential limits for -harmonic functions in the Sobolev space , for some , where is the unit ball in . Here is allowed to be different from .

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Additional Information

**Pekka Koskela**

Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109

Email:
pkoskela@math.jyu.fi

**Juan J. Manfredi**

Affiliation:
Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

Email:
manfredit@pitt.edu

**Enrique Villamor**

Affiliation:
Department of Mathematics, Florida International University, Miami, Florida 33199

Email:
villamor@fiu.edu

DOI:
https://doi.org/10.1090/S0002-9947-96-01430-4

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

Article copyright:
© Copyright 1996
American Mathematical Society