Result: On a shape derivative formula for star-shaped domains using Minkowski deformation
Title:
On a shape derivative formula for star-shaped domains using Minkowski deformation
Authors:
Contributors:
Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ), Laboratoire de Mathématiques et Applications, Laboratoire de mathématiques et applications, Université Cadi Ayyad Marrakech (UCA)-Faculté des sciences et techniques de Beni-Mellal, CNRSCampus France
Source:
AIMS Mathematics, Vol 8, Iss 8, Pp 19773-19793 (2023)
Publisher Information:
American Institute of Mathematical Sciences (AIMS), 2023.
Publication Year:
2023
Subject Terms:
volume functional, Spatial Point Patterns in Science, Inverse Problems in Mathematical Physics and Imaging, sup- port function, Geometry, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], Mathematical analysis, support function, Meteorology, Convex body, gauge function, QA1-939, FOS: Mathematics, starshaped domain, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], star-shaped domain, Mathematical Physics, Convex Bodies, convex domain, Minkowski space, Extension (predicate logic), Deformation (meteorology), Applied Mathematics, Physics, Pure mathematics, Iterative Algorithms for Nonlinear Operators and Optimization, Mixed volume, 16. Peace & justice, Brunn-Minkowski, Computer science, Convex optimization, Programming language, Regular polygon, Computational Theory and Mathematics, Combinatorics, brunn-minkowski theory, shape optimization, Physical Sciences, Computer Science, shape derivative, Minkowski deformation, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], minkowski deformation, Mathematics, Star (game theory)
Document Type:
Academic journal
Article<br />Other literature type<br />Report
ISSN:
2473-6988
DOI:
10.3934/math.20231008
DOI:
10.60692/37711-bd141
DOI:
10.60692/dfkym-vf866
Accession Number:
edsair.doi.dedup.....852f1b2e6551e35b93f97c111e8a847f
Database:
OpenAIRE
Further Information
We consider the shape derivative formula for a volume cost functional studied in previous papers where we used the Minkowski deformation and support functions in the convex setting. In this work, we extend it to some non-convex domains, namely the star-shaped ones. The formula happens to be also an extension of a well-known one in the geometric Brunn-Minkowski theory of convex bodies. At the end, we illustrate the formula by applying it to some model shape optimization problem.