**Francesca Crispo** ^{[1]} and **Paolo Maremonti** ^{[1]}

*On the higher regularity of solutions to the \(p\)-Laplacean system in the subquadratic case*

**Pages:** 39-63

**Received:** 5 April 2013

**Accepted:** 13 May 2013

**Mathematics Subject Classification (2010):** 35J92, 35J55, 35B65.

**Keywords:** \(p\)-Laplacean, higher integrability, global regularity.

**Authors address:**

[1] : Second University of Naples, Via Vivaldi 43, Caserta, 81100, Italy

**Abstract:**
We study the regularity properties of solutions to the
non-homogeneous \(p\)-Laplacean system, \(p\in (1,2)\), in a bounded
domain \(\Omega\). Under suitable restrictions on the exponent \(p\), we
construct a \(W_0^{1,2}(\Omega)\cap W^{ 2,2}(\Omega)\) solution. Then we prove
higher integrability results of the second-order derivatives of the
solution. Finally, by means of semigroup properties of solutions to
a special parabolic system, we prove a global pointwise bound for
weak solutions under the only assumption \(p\in\Big(\displaystyle\frac{2n}{n+2}, 2\Big)\).

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