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Zeitschrift für Analysis und ihre Anwendungen


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Volume 38, Issue 2, 2019, pp. 191–208
DOI: 10.4171/ZAA/1634

Published online: 2019-04-09

Partial Regularity of Solutions of Nonlinear Superelliptic Systems with Subquadratic Growth

Christoph Hamburger[1]

(1) Universität Bonn, Germany

We prove global partial regularity of weak solutions $u$ of the Dirichlet problem for the nonlinear superelliptic system div $A(x,u,Du) + B(x,u,Du) = 0$, under natural subquadratic polynomial growth of the coefficient functions $A$ and $B$. We employ the indirect method of the bilinear form and do not use a Caccioppoli or a reverse Hölder inequality.

Keywords: Partial regularity, boundary regularity, weak solution, nonlinear system, Dirichlet problem, ellipticity, subquadratic growth

Hamburger Christoph: Partial Regularity of Solutions of Nonlinear Superelliptic Systems with Subquadratic Growth. Z. Anal. Anwend. 38 (2019), 191-208. doi: 10.4171/ZAA/1634