Traces and fine properties of a \(BD\) class of vector fields and applications

DOI10.5802/afst.1102zbMath1091.35007OpenAlexW2332888487MaRDI QIDQ819894

Gianluca Crippa, Stefania Maniglia, Luigi Ambrosio

Publication date: 30 March 2006

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AFST_2005_6_14_4_527_0

zbMATH Keywords

finite deformationbounded deformationDiPerna-Lions theory

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Linear first-order PDEs (35F05)

Related Items (37)

Rigidity and trace properties of divergence-measure vector fields ⋮ On BV functions and essentially bounded divergence-measure fields in metric spaces ⋮ The jump set under geometric regularisation. II: Higher-order approaches ⋮ The prescribed mean curvature equation in weakly regular domains ⋮ The Flow Associated to Weakly Differentiable Vector Fields: Recent Results and Open Problems ⋮ Gauss‐Green theorem for weakly differentiable vector fields, sets of finite perimeter, and balance laws ⋮ Renormalization for Autonomous Nearly Incompressible BV Vector Fields in Two Dimensions ⋮ Steady nearly incompressible vector fields in two-dimension: chain rule and renormalization ⋮ New Regularity Results for Scalar Conservation Laws, and Applications to a Source-Destination Model for Traffic Flows on Networks ⋮ On locally essentially bounded divergence measure fields and sets of locally finite perimeter ⋮ Well posedness of ODE's and continuity equations with nonsmooth vector fields, and applications ⋮ Representation formulas for pairings between divergence-measure fields and \(BV\) functions ⋮ Traces and extensions of bounded divergence-measure fields on rough open sets ⋮ L1-Theory for Hele-Shaw flow with linear drift ⋮ Finite energy solutions for nonlinear elliptic equations with competing gradient, singular and \(L^1\) terms ⋮ Strong solutions to a parabolic equation with linear growth with respect to the gradient variable ⋮ Anzellotti's pairing theory and the Gauss-Green theorem ⋮ Wellposedness in the Lipschitz class for a quasi-linear hyperbolic system arising from a model of the atmosphere including water phase transitions ⋮ Plane-like minimizers and differentiability of the stable norm ⋮ Initial-boundary value problems for continuity equations with BV coefficients ⋮ An extension of the pairing theory between divergence-measure fields and BV functions ⋮ Shape derivatives for minima of integral functionals ⋮ Existence and uniqueness of maximal regular flows for non-smooth vector fields ⋮ Cauchy fluxes and Gauss-Green formulas for divergence-measure fields over general open sets ⋮ Initial-boundary value problems for nearly incompressible vector fields, and applications to the Keyfitz and Kranzer system ⋮ On the chain rule formulas for divergences and applications to conservation laws ⋮ Transport equation and image interpolation with SBD velocity fields ⋮ Stability of flows associated to gradient vector fields and convergence of iterated transport maps ⋮ The Gauss-Green theorem in stratified groups ⋮ Nonlinear diffusion in transparent media: the resolvent equation ⋮ Rough traces of BV functions in metric measure spaces ⋮ Initial-boundary value problems for merely bounded nearly incompressible vector fields in one space dimension ⋮ A uniqueness result for the decomposition of vector fields in \(\mathbb{R}^d\) ⋮ Weak-strong uniqueness for a class of generalized dissipative weak solutions for non-homogeneous, non-Newtonian and incompressible fluids ⋮ A phase-field approach to Eulerian interfacial energies ⋮ A Note on Two-Dimensional Transport with Bounded Divergence ⋮ Pairings between bounded divergence-measure vector fields and BV functions

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