Distributed and boundary expressions of first and second order shape derivatives in nonsmooth domains

Journal de Mathématiques Pures et Appliquées ◽

10.1016/j.matpur.2019.09.002 ◽

2020 ◽

Vol 134 ◽

pp. 328-368

Author(s):

Antoine Laurain

Keyword(s):

Second Order ◽

Shape Derivatives ◽

Nonsmooth Domains

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A Variational Method for Second Order Shape Derivatives

SIAM Journal on Control and Optimization ◽

10.1137/15100494x ◽

2016 ◽

Vol 54 (2) ◽

pp. 1056-1084 ◽

Author(s):

Guy Bouchitté ◽

Ilaria Fragalà ◽

Ilaria Lucardesi

Keyword(s):

Variational Method ◽

Second Order ◽

Shape Derivatives

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Estimates of first and second order shape derivatives in nonsmooth multidimensional domains and applications

Journal of Functional Analysis ◽

10.1016/j.jfa.2016.02.013 ◽

2016 ◽

Vol 270 (7) ◽

pp. 2616-2652 ◽

Author(s):

Jimmy Lamboley ◽

Arian Novruzi ◽

Michel Pierre

Keyword(s):

Second Order ◽

Shape Derivatives

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Second order directional shape derivatives of integrals on submanifolds

Mathematical Control & Related Fields ◽

10.3934/mcrf.2021017 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Anton Schiela ◽

Julian Ortiz

Keyword(s):

Second Order ◽

Shape Derivatives ◽

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Dini continuity of the first derivatives of generalized solutions to the Dirichlet problem for linear elliptic second order equations in nonsmooth domains

Annales Polonici Mathematici ◽

10.4064/ap-69-2-129-154 ◽

1998 ◽

Vol 69 (2) ◽

pp. 129-154 ◽

Author(s):

Michail Borsuk

Keyword(s):

Dirichlet Problem ◽

Second Order ◽

Generalized Solutions ◽

Nonsmooth Domains ◽

Derivatives Of ◽

Second Order Equations

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Passive Control of Singularities by Topological Optimization: The Second-Order Mixed Shape Derivatives of Energy Functionals for Variational Inequalities

Springer Optimization and Its Applications - Advances in Mathematical Modeling, Optimization and Optimal Control ◽

10.1007/978-3-319-30785-5_4 ◽

2016 ◽

pp. 65-102

Author(s):

Günter Leugering ◽

Jan Sokołowski ◽

Antoni Żochowski

Keyword(s):

Variational Inequalities ◽

Passive Control ◽

Second Order ◽

Topological Optimization ◽

Energy Functionals ◽

Shape Derivatives ◽

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Second-order shape derivatives along normal trajectories, governed by Hamilton-Jacobi equations

Structural and Multidisciplinary Optimization ◽

10.1007/s00158-016-1514-2 ◽

2016 ◽

Vol 54 (5) ◽

pp. 1245-1266 ◽

Author(s):

G. Allaire ◽

E. Cancès ◽

J.-L. Vié

Keyword(s):

Second Order ◽

Shape Derivatives ◽

Jacobi Equations

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Weights and Hölder norms for solutions to a second order elliptic Dirichlet problem on nonsmooth domains

Harmonic Analysis, Partial Differential Equations, and Related Topics - Contemporary Mathematics ◽

10.1090/conm/428/08217 ◽

2007 ◽

pp. 127-138

Author(s):

Caroline Sweezy

Keyword(s):

Dirichlet Problem ◽

Second Order ◽

Nonsmooth Domains

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Hölder Regularity of Solutions to Second-Order Elliptic Equations in Nonsmooth Domains

Boundary Value Problems ◽

10.1155/2007/57928 ◽

2007 ◽

Vol 2007 ◽

pp. 1-24 ◽

Author(s):

Sungwon Cho ◽

Mikhail Safonov

Keyword(s):

Elliptic Equations ◽

Second Order ◽

Regularity Of Solutions ◽

Hölder Regularity ◽

Nonsmooth Domains ◽

Second Order Elliptic Equations ◽

Holder Regularity

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$L^2$-Integrability of Second Order Derivatives for Poisson's Equation in Nonsmooth Domains.

MATHEMATICA SCANDINAVICA ◽

10.7146/math.scand.a-12391 ◽

1992 ◽

Vol 70 ◽

pp. 146 ◽

Author(s):

Vilhelm Adolfsson

Keyword(s):

Second Order ◽

Poisson’S Equation ◽

Poisson's Equation ◽

Nonsmooth Domains

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Degenerate elliptic boundary-value problems of second order in nonsmooth domains

Journal of Mathematical Sciences ◽

10.1007/s10958-007-0470-1 ◽

2007 ◽

Vol 146 (5) ◽

pp. 6071-6212 ◽

Author(s):

Mikhail Borsuk

Keyword(s):

Boundary Value Problems ◽

Elliptic Boundary ◽

Boundary Value ◽

Second Order ◽

Elliptic Boundary Value Problems ◽

Elliptic Boundary Value ◽

Nonsmooth Domains ◽

Degenerate Elliptic

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