Partial Regularity of Solutions of Nonlinear Superelliptic Systems with Subquadratic Growth

Christoph Hamburger

doi:10.4171/zaa/1634

JournalszaaVol. 38, No. 2pp. 191–208

Partial Regularity of Solutions of Nonlinear Superelliptic Systems with Subquadratic Growth

Christoph Hamburger
Universität Bonn, Germany

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Abstract

We prove global partial regularity of weak solutions $u$ of the Dirichlet problem for the nonlinear superelliptic system div $A (x, u, D u) + B (x, u, D u) = 0$ , 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.

Cite this article

Christoph Hamburger, Partial Regularity of Solutions of Nonlinear Superelliptic Systems with Subquadratic Growth. Z. Anal. Anwend. 38 (2019), no. 2, pp. 191–208

DOI 10.4171/ZAA/1634