On some sharp bounds for the homogenized p-poisson equation

Abstract

We consider homogenization of a scale of p-Poisson equations in R^N. Some new bounds of the effective energy are proved and compared with the non-linear Wiener -and Hashin-Shtrikman bounds. Moreover, we point out concrete nontrivid examples where these bounds even coincide. Some new examples of “optimal” microstructures are presented.

Keywords:

• p-Poisson equation
• Homogenization
• effective energy
• bounds
• optimal structures
• means

AMS:

• 35Q35
• 35J20

Additional information

Notes on contributors

Dag Lukkassen

Lar Erik Persson

Peter Wall