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- W3104730266 abstract "We present a way to study a wide class of optimal design problems with a perimeter penalization. More precisely, we address existence and regularity properties of saddle points of energies of the form $$ (u,A) quad mapsto quad int_Omega 2fu ; text{d}x ; - int_{Omega cap A} sigma_1 mathscr A u cdot mathscr A u ; text{d}x ; - int_{Omega setminus A} sigma_2mathscr A ucdot mathscr A u ; text{d}x ; + ; text{Per}(A;overline Omega),$$ where $Omega$ is a bounded Lipschitz domain, $Asubset mathbb R^N$ is a Borel set, $u:Omega subset mathbb R^N to mathbb R^d$, $mathscr A$ is an operator of gradient form, and $sigma_1, sigma_2$ are two not necessarily well-ordered symmetric tensors. The class of operators of gradient form includes scalar- and vector-valued gradients, symmetrized gradients, and higher order gradients. Therefore, our results may be applied to a wide range of problems in elasticity, conductivity or plasticity models. In this context and under mild assumptions on $f$, we show for a solution $(w,A)$, that the topological boundary of $A cap Omega$ is locally a $rm{C}^1$-hypersurface up to a closed set of zero $mathscr H^{N-1}$-measure." @default.
- W3104730266 created "2020-11-23" @default.
- W3104730266 creator A5010511076 @default.
- W3104730266 date "2016-11-30" @default.
- W3104730266 modified "2023-09-25" @default.
- W3104730266 title "Regularity for free interface variational problems in a general class of gradients" @default.
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- W3104730266 doi "https://doi.org/10.1007/s00526-016-1085-5" @default.
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