A version of Stokes's theorem using test curves

DOI10.1512/iumj.2020.69.8389zbMath1461.26005OpenAlexW3007691741MaRDI QIDQ5109027

Olli Martio, Jan Malý, Vendula Honzlová Exnerová

Publication date: 7 May 2020

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10138/314791

zbMATH Keywords

functions of bounded variationStokes theoremdivergence theoremAM-modulus

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Lipschitz (Hölder) classes (26A16) Length, area, volume, other geometric measure theory (28A75) Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.) (26B20) Currents in global analysis (58A25)

Cites Work

• Functions of bounded variation and curves in metric measure spaces
• Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
• On the duality between \(p\)-modulus and probability measures
• Extremal length and functional completion
• Cauchy flux and sets of finite perimeter
• Cauchy's stress theorem for stresses represented by measures
• Functions of bounded variation and the \(AM\)-modulus in \(\mathbb{R}^n\)
• Modulus in Banach function spaces
• Equivalent definitions of \(BV\) space and of total variation on metric measure spaces
• Divergence measure fields and Cauchy's stress theorem
• Confromal invariants and function-theoretic null-sets
• The space of functions of bounded variation on curves in metric measure spaces
• Moduli in Modern Mapping Theory
• Weakly Differentiable Functions
• The Divergence Theorem for Divergence Measure Vectorfields on Sets with Fractal Boundaries
• Gauss‐Green theorem for weakly differentiable vector fields, sets of finite perimeter, and balance laws
• Über den Gaußschen und den Stokesschen Integralsatz. I
• Über den Gaußschen und den Stokesschen Integralsatz. II
• Über den Gaußschen und den Stokesschen Integralsatz. III
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