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A variational method for second order shape derivatives

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arxiv 1509.00178 v1 pith:I6PPXTWI submitted 2015-09-01 math.OC

Guy Bouchitté , Ilaria Fragalà , Ilaria Lucardesi This is my paper · ORCID
classification math.OC
keywords shapeconsiderfunctionalsordersecondapproachboundaryclassical
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We consider shape functionals obtained as minima on Sobolev spaces of classical integrals having smooth and convex densities, under mixed Dirichlet-Neumann boundary conditions. We propose a new approach for the computation of the second order shape derivative of such functionals, yielding a general existence and representation theorem. In particular, we consider the p-torsional rigidity functional for p grater than or equal to 2.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 8 citations worldwide. Full citation record

  1. Mixed Torsion on Right Triangles and the P\'olya--Szeg\H{o} Monotonicity Problem for Regular Polygons

    math.AP 2026-06 unverdicted novelty 7.0 of 10

    Proves mixed torsional rigidity increases with Neumann/Dirichlet leg ratio on right triangles and T^D(P_{N+1}) > T^D(P_N) for regular polygons of area π, plus asymptotic expansion.

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