Three examples of residual pathologies

DOI10.1007/s11537-023-2041-8arXiv1908.09496OpenAlexW4362604276MaRDI QIDQ6156880

Massimo Gobbino, Marina Ghisi

Publication date: 19 June 2023

Published in: Japanese Journal of Mathematics. 3rd Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.09496

zbMATH Keywords

wave equationHölder continuitytransport equationultradistributionsBaire categoryresidual setGevrey spacesapproximately differentiable functionderivative loss

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Turbulent transport, mixing (76F25) Initial value problems for second-order hyperbolic equations (35L15)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Non-uniqueness for the transport equation with Sobolev vector fields
• Transport equation and Cauchy problem for BV vector fields
• On admissibility criteria for weak solutions of the Euler equations
• Linear wave equations with time-dependent propagation speed and strong damping
• Equidimensional isometric maps
• Ordinary differential equations, transport theory and Sobolev spaces
• The Euler equations as a differential inclusion
• On the Dirichlet problem for first order partial differential equations. A Baire category approach
• General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases
• On the Frisch-Parisi conjecture
• Multifractal properties of typical convex functions
• Time-dependent propagation speed vs strong damping for degenerate linear hyperbolic equations
• Critical counterexamples for linear wave equations with time-dependent propagation speed
• Sharp regularity estimates for solutions of the continuity equation drifted by Sobolev vector fields
• Loss of regularity for the continuity equation with non-Lipschitz velocity field
• Long-time instability and unbounded Sobolev orbits for some periodic nonlinear Schrödinger equations
• Existence of infinitely many solutions for the one-dimensional Perona-Malik model
• Deformations with finitely many gradients and stability of quasiconvex hulls
• Generalized subdifferentials: a Baire categorical approach
• High dimensionality and h-principle in PDE
• Fourier Analysis and Nonlinear Partial Differential Equations
• Derivative loss for Kirchhoff equations with non-Lipschitz nonlinear term
• Baire category and the weak bang-bang property for continuous differential inclusions
• Besicovitch via Baire
• The Concept of Varifold
• Exponential self-similar mixing by incompressible flows
• The ℎ-principle and the equations of fluid dynamics
• Distance functions with dense singular sets
• Continuity equations and ODE flows with non-smooth velocity
• Convex Integration and Infinitely Many Weak Solutions to the Perona--Malik Equation in All Dimensions
• Convex Bodies The Brunn-MinkowskiTheory
• Comparing two methods of resolving homogeneous differential inclusions