Homogenization of High-contrast Mumford--Shah Energies
نویسندگان
چکیده
منابع مشابه
Homogenization of Discrete High-Contrast Energies
Variational theories of double-porosity models can be derived by homogenization of high-contrast periodic media (see [12]). Typically, we have one or more strong phases (i.e., uniformly elliptic energies on periodic connected domains) and a weak phase with a small ellipticity constant, coupled with some lower-order term. In the simplest case of quadratic energies, this amounts to considering en...
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We want to understand he concentration of damage in microfractured elastic media. Due to the different scallings of the volume and area (or area and length in two dimensions) the traditional method of homogenization using periodic arrays of cells seems to fail when applied to the Mumford-Shah functional and to periodically fractured domains. In the present paper we are departing from traditiona...
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Ω |∇u| dx+ cH(Su) where u ∈ SBV (Ω), the space of special functions of bounded variation; Su is the approximate discontinuity set of u and Hn−1 is the (n− 1)-dimensional Hausdorff measure. Several approximation methods are known for the MumfordShah functional and, more in general, for free discontinuity functionals: the Ambrosio & Tortorelli approximation (see [1] and [3]) via elliptic function...
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ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 2019
ISSN: 0036-1410,1095-7154
DOI: 10.1137/18m1189804