Partial Regularity of Solutions of Nonlinear Superelliptic Systems with Subquadratic Growth

Partial Regularity of Solutions of Nonlinear Superelliptic Systems with Subquadratic Growth

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 n...

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Veröffentlicht in:Zeitschrift für Analysis und ihre Anwendungen 2019-01, Vol.38 (2), p.191-208
1. Verfasser: Hamburger, Christoph
Format: Artikel
Sprache:eng
Schlagworte:
Equality
Partial differential equations
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Zusammenfassung: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.
ISSN:0232-2064
1661-4534
DOI:10.4171/ZAA/1634