Electron. J. Diff. Eqns., Vol. 2006(2006), No. 49, pp. 1-10.

Nonlinear elastic membranes involving the p-Laplacian operator

Fabrizio Cuccu, Behrouz Emamizadeh, Giovanni Porru

Abstract:
This paper concerns an optimization problem related to the Poisson equation for the p-Laplace operator, subject to homogeneous Dirichlet boundary conditions. Physically the Poisson equation models, for example, the deformation of a nonlinear elastic membrane which is fixed along the boundary, under load. A particular situation where the load is represented by a characteristic function is investigated.

Submitted February 2, 2006. Published April 14, 2006.
Math Subject Classifications: 35J20, 35B38, 49Q10.
Key Words: p-Laplace; rearrangements; maximum principle; existence; uniqueness; domain derivative.

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Fabrizio Cuccu
Mathematics Department
Universitá di Cagliari
Via Ospedale 72, 09124 Cagliari, Italy
email: fcuccu@unica.it
Behrouz Emamizadeh
Department of Mathematics
The Petroleum Institute
P. O. Box 2533, Abu Dhabi, UAE
email: bemamizadeh@pi.ac.ae
Giovanni Porru
Mathematics Department
Universitá di Cagliari
Via Ospedale 72, 09124 Cagliari, Italy
email: porru@unica.it

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