Lower semicontinuity in \(L^1\) of a class of functionals defined on \(BV\) with Carathéodory integrands

DOI10.1155/2021/6709303zbMath1497.49020OpenAlexW3214907250MaRDI QIDQ2675675

Thomas Wunderli

Publication date: 24 September 2022

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2021/6709303

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Variational inequalities (49J40) Methods involving semicontinuity and convergence; relaxation (49J45) Duality theory (optimization) (49N15) Absolutely continuous real functions of several variables, functions of bounded variation (26B30)

Cites Work

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• Lower semicontinuity and relaxation of signed functionals with linear growth in the context of \(\mathcal A\)-quasiconvexity
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• Characterization of generalized gradient Young measures generated by sequences in \(W^{1,1}\) and BV
• Convex functionals and partial regularity
• Parabolic quasilinear equations minimizing linear growth functionals
• Liftings, Young measures, and lower semicontinuity
• On functionals with convex Carathéodory integrands with a linear growth condition
• Lower semicontinuity and \(\varGamma \)-convergence of a class of linear growth functionals
• Convex duality and uniqueness for BV-minimizers
• The Euler Equation for Functionals with Linear Growth
• Variable Exponent, Linear Growth Functionals in Image Restoration

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