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Zeitschrift für Analysis und ihre Anwendungen


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Volume 39, Issue 3, 2020, pp. 315–347
DOI: 10.4171/ZAA/1662

Published online: 2020-07-06

Partial Regularity Results for Quasimonotone Elliptic Systems with General Growth

Bianca Stroffolini[1]

(1) Università degli Studi di Napoli Federico II, Italy

We present a partial Hölder regularity result for the gradient of solutions to quasimonotone systems: $$\mathrm div \:\mathbf A(\cdot,D\mathbf u) = \mathbf B(\cdot, D\mathbf u) \quad \text{in } \Omega,$$ on bounded domains in the weak sense. Here certain continuity, uniformly strictly quasimonotonicity, growth conditions are imposed on the coefficients, including an asymptotic Uhlenbeck behaviour close to the origin, while the inhomogeneous term satis es controllable growth conditions. The result is achieved along a two-scale regime: degenerate and non-degenerate. In particular, we will use approximation lemmas, Diening et al. [J. Diff. Equ. 253 (2012)(7), 1943–1958; SIAM J. Math. Anal. 44 (2012)(5), 3594–3616], that simplify and unify the proof in the power growth case and allow us to consider also the general growth case.

Keywords: Partial regularity, quasimonotone systems, general growth

Stroffolini Bianca: Partial Regularity Results for Quasimonotone Elliptic Systems with General Growth. Z. Anal. Anwend. 39 (2020), 315-347. doi: 10.4171/ZAA/1662