Nonlinear open mapping principles, with applications to the Jacobian equation and other scale-invariant PDEs

DOI10.1016/j.aim.2023.108869OpenAlexW3094236367MaRDI QIDQ2684524

Lukas Koch, Sauli Lindberg, André Guerra

Publication date: 16 February 2023

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.10497

zbMATH Keywords

Hardy spaceincompressible Euler equationsJacobian equationopen mapping principle

Mathematics Subject Classification ID

Partial differential equations of mathematical physics and other areas of application (35Q99) Nonlinear operators and their properties (47H99) Euler equations (35Q31)

Related Items

A note on the Jacobian problem of Coifman, Lions, Meyer and Semmes, On the topological size of the class of Leray solutions with algebraic decay

Cites Work

• On certain uniformly open multilinear mappings
• Lectures on mappings of finite distortion
• Openness of multiplication in some function spaces
• Solution of the Dirichlet problem for the prescribed Jacobian equation using the Monge-Ampère equation
• On the Hardy space theory of compensated compactness quantities
• Existence of weak solutions for the incompressible Euler equations
• The pullback equation for differential forms
• An inviscid flow with compact support in space-time
• The global Cauchy problem for the nonlinear Klein-Gordon equation
• On admissibility criteria for weak solutions of the Euler equations
• On a partial differential equation involving the Jacobian determinant
• The Euler equations as a differential inclusion
• On the equation \(\det\nabla{u}=f\) with no sign hypothesis
• Note on property \(({\mathbb{A}}_ 1)\)
• Property N for the space mappings of class \(W^ 1_{n,loc}\)
• Factorization theorems for Hardy spaces in several variables
• Nonlinear commutators and Jacobians
• Separated nets in Euclidean space and Jacobians of biLipschitz maps
• Lipschitz maps and nets in Euclidean space
• Convex integration for Lipschitz mappings and counterexamples to regularity
• A proof of Onsager's conjecture
• Degraded mixing solutions for the Muskat problem
• Lusin's condition (N) and mappings with nonnegative Jacobians
• A counterexample to the closed graph theorem for bilinear maps
• Compensated compactness and Hardy spaces
• Resolutions of the prescribed volume form equation
• Limiting Sobolev inequalities for vector fields and canceling linear differential operators
• Convex integration with constraints and applications to phase transitions and partial differential equations
• Energy minimisers with prescribed Jacobian
• On the necessity of the constant rank condition for \(L^p\) estimates
• Young measures generated by ideal incompressible fluid flows
• Potentials for \(\mathcal {A}\)-quasiconvexity
• On the product of functions in BMO and H\(^1\)
• Sur la méthode de résonance et sur un théorème concernant les espaces de type \(\{(B)\}\)
• The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces
• Weak solutions of ideal MHD which do not conserve magnetic helicity
• Nonlinear Cauchy-Riemann operators in ℝⁿ
• Hierarchical Construction of Bounded Solutions in Critical Regularity Spaces
• Fourier Analysis and Nonlinear Partial Differential Equations
• The Three-Dimensional Navier–Stokes Equations
• Higher integrability of determinants and weak convergence in L1.
• The Radon-Nikodym Property in Conjugate Banach Spaces. II
• Polar factorization and monotone rearrangement of vector‐valued functions
• An Elementary Counterexample to the Open Mapping Principle for Bilinear Maps
• Extensions of Hardy spaces and their use in analysis
• Generalized Open Mapping Theorems for Bilinear Maps, with an Application to Operator Algebras
• On Mappings with Integrable Dilatation
• Lusin's condition (N) and mappings of the class W1, n.
• Rigidity for the four gradient problem
• On the equation 𝑑𝑖𝑣𝑌=𝑓 and application to control of phases
• The ℎ-principle and the equations of fluid dynamics
• On turbulence and geometry: from Nash to Onsager
• Convex integration constructions in hydrodynamics
• Nonuniqueness of Weak Solutions to the SQG Equation
• On the Volume Elements on a Manifold
• The geometric integration of scale-invariant ordinary and partial differential equations
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