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 to
is sufficient for continuity of u, but not for \({\epsilon=0}\).
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Jiang, R., Koskela, P. & Yang, D. Continuity of solutions to n-harmonic equations. manuscripta math. 139, 237–248 (2012). https://doi.org/10.1007/s00229-011-0514-1
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DOI: https://doi.org/10.1007/s00229-011-0514-1