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- W1911858502 abstract "In this paper, we are interested in shape optimization problems involving the ge ometry (normal, curvatures) of the surfaces. We consider a class of hypersurface s in $mathbb{R}^{n}$ satisfying a uniform ball condition and we prove the exist ence of a $C^{1,1}$-regular minimizer for general geometric functionals and cons traints involving the first- and second-order properties of surfaces, such as in $mathbb{R}^{3}$ problems of the form: $$ inf int_{partial Omega} j_0 [ mathbf{x},mathbf{n}(mathbf{x}) ] dA (mathbf{x}) + int_{partial Omega} j_1 [ mathbf{x},mathbf{n}(mathbf{x}),H(mathbf{x}) ] dA (mathbf{x}) + int_{partial Omega} j_2 [mathbf{x},mathbf{n}(mathbf{x}),K(mathbf{x})] dA (mathbf{x}), $$ where $mathbf{n}$, $H$, and $K$ respectively denotes the normal, the scalar mea n curvature and the Gaussian curvature. We gives some various applications in th e modelling of red blood cells such as the Canham-Helfrich energy and the Willmo re functional." @default.
- W1911858502 created "2016-06-24" @default.
- W1911858502 creator A5075684738 @default.
- W1911858502 date "2015-04-16" @default.
- W1911858502 modified "2023-10-06" @default.
- W1911858502 title "Uniform ball property and existence of optimal shapes for a wide class of geometric functionals" @default.
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