Riv. Mat. Univ. Parma, Vol. 5, No. 1, 2014

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
Accepted: 13 May 2013
Mathematics Subject Classification (2010): 35J92, 35J55, 35B65.

Keywords: $$p$$-Laplacean, higher integrability, global regularity.
[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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