Estimates of Jacobians by subdeterminants.

DOI10.1007/BF02922041zbMath1053.42024WikidataQ110031917 ScholiaQ110031917MaRDI QIDQ1608529

Jani Onninen, Anna Verde, Flavia Giannetti, Tadeusz Iwaniec

Publication date: 8 August 2002

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

zbMATH Keywords

Orlicz spacedistributional Jacobiancofactor matrixintegrability of Jacobians

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Maximal functions, Littlewood-Paley theory (42B25) Implicit function theorems, Jacobians, transformations with several variables (26B10)

Related Items

Mappings of finite distortion: sharp Orlicz-conditions ⋮ Mappings of finite distortion: The sharp modulus of continuity ⋮ On grand and small Lebesgue and Sobolev spaces and some applications to PDE's ⋮ Luzin's condition (N) and Sobolev mappings ⋮ A version of Gehring lemma in Orlicz spaces ⋮ An integral form of the isoperimetric inequality ⋮ On the product of functions in BMO and H\(^1\) ⋮ Mappings of finite distortion: minors of the differential matrix ⋮ Deformations of finite conformal energy: Boundary behavior and limit theorems ⋮ Elliptic problems with growth in nonreflexive Orlicz spaces and with measure or \(L^1\) data

Cites Work

• Regularity properties of deformations with finite energy
• On the integrability of the Jacobian under minimal hypotheses
• Convexity conditions and existence theorems in nonlinear elasticity
• A remark on the equality \(\text{det} Df=\text{Det} Df\)
• Integrability for the Jacobian of orientation preserving mappings
• \({\mathcal H}^1\)-estimates of Jacobians by subdeterminants
• Compensated compactness and Hardy spaces
• On a new class of elastic deformations not allowing for cavitation
• A note on weak approximation of minors
• Some geometrical properties of functions and mappings with generalized derivatives
• Minimal assumptions for the integrability of the Jacobian
• Higher integrability of determinants and weak convergence in L1.
• A study of Jacobians in Hardyd–Orlicz spaces
• Limits of the improved integrability of the volume forms
• Invertibility and a Topological Property of Sobolev Maps
• Direct methods in the calculus of variations
• Mappings of finite distortion: Monotonicity and continuity
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item