On a singular variational integral with linear growth. I: Existence and regularity of minimizers

DOI10.1007/BF00281248zbMath0651.49017MaRDI QIDQ1106463

Josef Bemelmans, Ulrich Dierkes

Publication date: 1987

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

zbMATH Keywords

regularityvariational integrallinear growthexistence of a minimizer

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems in a geometric measure-theoretic setting (49Q20) Geometric measure and integration theory, integral and normal currents in optimization (49Q15)

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Cites Work

• The imbedding problem for Riemannian manifolds
• Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in \(n\) variabili
• Integral representation on \(BV(\Omega )\) of \(\Gamma\)-limits of variational integrals
• The two-dimensional analogue of the catenary
• Regularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals
• A NONEXISTENCE THEOREM FOR THE TWO-DIMENSIONAL AMLOGUE OF THE CATENARY
• Gleichgewichtsfiguren zäher Flüssigkeiten mit Oberflächenspannung
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