An extensive study of the regularity of solutions to doubly singular equations
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Vincenzo Vespri
Abstract
In recent years, many papers have been devoted to the regularity of doubly nonlinear singular evolution equations. Many of the proofs are unnecessarily complicated, rely on superfluous assumptions or follow an inappropriate approximation procedure. This makes the theory unclear and quite chaotic to a nonspecialist. The aim of this paper is to fix all the misprints, to follow correct procedures, to exhibit, possibly, the shortest and most elegant proofs and to give a complete and self-contained overview of the theory.
Acknowledgements
Matias Vestberg wants to express gratitude to the Academy of Finland. Moreover, we thank Juha Kinnunen for useful discussions and feedback during the writing of this article.
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Articles in the same Issue
- Frontmatter
- Michell truss type theories as a Γ-limit of optimal design in linear elasticity
- The local structure of the free boundary in the fractional obstacle problem
- Homogenization of quadratic convolution energies in periodically perforated domains
- Uniqueness and nonuniqueness of limits of Teichmüller harmonic map flow
- Regularity for minimizers of a class of non-autonomous functionals with sub-quadratic growth
- On a comparison principle for Trudinger’s equation
- Equivalence of ray monotonicity properties and classification of optimal transport maps for strictly convex norms
- An extensive study of the regularity of solutions to doubly singular equations
- New features of the first eigenvalue on negatively curved spaces
- High order curvature flows of plane curves with generalised Neumann boundary conditions
- (BV,L p )-decomposition, p = 1,2, of functions in metric random walk spaces
- Causal variational principles in the σ-locally compact setting: Existence of minimizers
- On sub-Riemannian geodesic curvature in dimension three
- Existence for singular critical exponential (𝑝, 𝑄) equations in the Heisenberg group
