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- Title
Continuity of solutions to n-harmonic equations.
- Authors
Jiang, Renjin; Koskela, Pekka; Yang, Dachun
- Abstract
In this paper, we study the nonhomogeneous n-harmonic equation in domains $${\Omega\subset {\mathbb {R}^n}}$$ ( n ≥ 2), where $${f\in W^{-1,\frac{n}{n-1}}(\Omega)}$$. We derive a sharp condition to guarantee the continuity of solutions u. In particular, we show that when n ≥ 3, the condition that, for some $${\epsilon >0 ,}$$ f belongs tois sufficient for continuity of u, but not for $${\epsilon=0}$$.
- Subjects
EQUATIONS; LAPLACE'S equation; HARMONIC analysis (Mathematics); MATHEMATICAL analysis; MATHEMATICS
- Publication
Manuscripta Mathematica, 2012, Vol 139, Issue 1/2, p237
- ISSN
0025-2611
- Publication type
Article
- DOI
10.1007/s00229-011-0514-1