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Optimal regularity for degenerate Kolmogorov equations in non-divergence form with rough-in-time coefficients
We consider a class of degenerate equations in non-divergence form satisfying a parabolic Hörmander condition, with coefficients that are measurable...
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Regularity of Minimizers
This chapter provides conditions under which minimizers for dynamic optimization problems possess regularity properties of interest, such as...
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The time-like minimal surface equation in Minkowski space: low regularity solutions
It has long been conjectured that for nonlinear wave equations that satisfy a nonlinear form of the null condition, the low regularity well-posedness...
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Further Regularity Methods
We already saw the cancellation method in Chap. 4 for the asymptotic Lipschitz regularity of value...
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Maximal regularity
The present chapter is one of the central ones of this book project. Maximal regularity provides a link between the general theory of operator-valued...
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Hölder Regularity
This chapter presents some classical results from the regularity theory of uniformly elliptic PDEs and in particular those results related to Hölder...
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Boundary pointwise regularity and applications to the regularity of free boundaries
In this paper, we develop a series of boundary pointwise regularity for Dirichlet problems and oblique derivative problems. As applications, we give...
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Discrete Maximal Regularity
Maximal \(L^p\) -regularity is an important mathematical...
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Higher Regularity and Finite Time Blow-up to Nonlocal Pseudo-parabolic Equation with Conical Degeneration
This paper deals with the initial-boundary value problem to a nonlocal semilinear pseudo-parabolic equation with conical degeneration, which has been...
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Time Regularity for Local Weak Solutions of the Heat Equation on Local Dirichlet Spaces
We study the time regularity of local weak solutions of the heat equation in the context of local regular symmetric Dirichlet spaces. Under two basic...
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Time regularity of generalized Navier-Stokes equation with p(x,t)-power law
We show time regularity of weak solutions for unsteady motion equations of generalized Newtonian fluids described by p ( x , t )-power law for p ( x,t ) ⩾ (3 n ...
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Maximal Regularity
In this chapter, we address the issue of maximal regularity. More precisely, we provide a criterion on the ‘structure’ of the evolutionary equation...
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Geometric regularity theory for a time-dependent Isaacs equation
The purpose of this work is to produce a regularity theory for a class of parabolic Isaacs equations. Our techniques are based on approximation...
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Feature Engineering with Regularity Structures
We investigate the use of models from the theory of regularity structures as features in machine learning tasks. A model is a polynomial function of...
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A Semi-discrete First-Order Low Regularity Exponential Integrator for the “good” Boussinesq Equation Without Loss of Regularity
In this paper, we propose a semi-discrete first-order low regularity exponential-type integrator (LREI) for the “good” Boussinesq equation. It is...
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