Elastic energy of a convex body
Copyright policy )Elastic energy of a convex body
In this paper a Blaschke‐Santaló diagram involving the area, the perimeter and the elastic energy of planar convex bodies is considered. More precisely we give a description of set urn:x-wiley:0025584X:media:mana201400256:mana201400256-math-0001where A is the area, P is the perimeter and E is the elastic energy, that is a Willmore type energy in the plane. In order to do this, we investigate the following shape optimization problem: urn:x-wiley:0025584X:media:mana201400256:mana201400256-math-0002where is the class of convex bodies with fixed perimeter and is a parameter. Existence, regularity and geometric properties of solutions to this minimum problem are shown.
convex geometry, shape optimization., Willmore type energy, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Blaschke diagram, Metric Geometry (math.MG), Elastic energy, Convex sets in \(2\) dimensions (including convex curves), Elastic energy, Willmore type energy, convex geometry, Blaschke diagram, shape optimization, elastic energy, Length, area, volume and convex sets (aspects of convex geometry), Optimization of shapes other than minimal surfaces, Mathematics - Metric Geometry, Optimization and Control (math.OC), shape optimization, Inequalities and extremum problems involving convexity in convex geometry, FOS: Mathematics, [MATH.MATH-MG] Mathematics [math]/Metric Geometry [math.MG], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics - Optimization and Control
convex geometry, shape optimization., Willmore type energy, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Blaschke diagram, Metric Geometry (math.MG), Elastic energy, Convex sets in \(2\) dimensions (including convex curves), Elastic energy, Willmore type energy, convex geometry, Blaschke diagram, shape optimization, elastic energy, Length, area, volume and convex sets (aspects of convex geometry), Optimization of shapes other than minimal surfaces, Mathematics - Metric Geometry, Optimization and Control (math.OC), shape optimization, Inequalities and extremum problems involving convexity in convex geometry, FOS: Mathematics, [MATH.MATH-MG] Mathematics [math]/Metric Geometry [math.MG], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics - Optimization and Control
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