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Sharp Morrey regularity theory for a fourth order geometrical equation
This paper is a continuation of recent work by Guo-**ang-Zheng [10]. We deduce the sharp Morrey regularity theory for weak solutions to the fourth...
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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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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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Regularity of Solutions
We now present several regularity results concerning solutions to the (anisotropic) least gradient problem. Due to the linear growth of the...
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Invariant tori via higher order averaging method: existence, regularity, convergence, stability, and dynamics
Important information about the dynamical structure of a differential system can be revealed by looking into its invariant compact manifolds, such as...
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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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Mesh Regularity
Why are tetrahedra so suitable to serve as finite elements in our mesh? Because they are flexible: can take all sorts of shapes and sizes. This is...
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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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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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Discrete Maximal Regularity
Maximal \(L^p\) -regularity is an important mathematical...
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Existence and Regularity Results for Degenerate Parabolic Problems in the Presence of Strongly Increasing Regularizing Lower-Order Terms and Lm-Data/Dirac Mass
We study the existence and regularity results for degenerate parabolic problems in the presence of strongly increasing regularizing lower-order terms...
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Description of Weak-Type BMO-Regularity
The weak-type BMO-regularity property for couples of quasi-Banach lattices of measurable functions was recently introduced as a suitable substitute...
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Order continuity and regularity on vector lattices and on lattices of continuous functions
We give several characterizations of order continuous vector lattice homomorphisms between Archimedean vector lattices. We reduce the proofs of some...
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Castelnuovo–Mumford regularity of matrix Schubert varieties
Matrix Schubert varieties are affine varieties arising in the Schubert calculus of the complete flag variety. We give a formula for the...
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Besov regularity of inhomogeneous parabolic PDEs
We study the regularity of solutions of parabolic partial differential equations with inhomogeneous boundary conditions on polyhedral domains
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Regularity of the Flat Free Boundaries
This chapter is dedicated to the regularity of the flat free boundaries. In particular, we will show how the improvement of flatness (proved in...