Optimal design problems in rough inhomogeneous media. Existence theory

Details Optimal design problems in rough inhomogeneous media. Existence theory Optimal design problems in rough inhomogeneous media. Existence theory

2007-10-16

arxiv.org/abs/0710.2936v2

Mathematics

Analysis of PDEs

Scientific paper

This paper settles the existence question for a rather general class of convex optimal design problems with a volume constraint. In low dimensions, we prove the existence of an optimal configuration for general convex minimization problems ruled by bounded measurable degenerate elliptic operators. Under a mild continuity assumption on the medium, the free boundary is proven to enjoy the appropriate weak geometry and we establish the existence of an optimal design for general convex optimal design problems with volume constraints for all dimensions.

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