Optimal design problems in rough inhomogeneous media. Existence theory∗
نویسنده
چکیده
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.
منابع مشابه
OPTIMAL DESIGN PROBLEMS IN ROUGH INHOMOGENEOUS MEDIA: EXISTENCE THEORY By EDUARDO
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 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 have an appropriate w...
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