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Logarithmic Hölder Continuous Map**s and Beltrami Equation
The results of this chapter were obtained together with S. Skvortsov. The chapter is devoted to the study of map**s satisfying the inverse Poletsky...
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Hölder Parameterization of Continuous Quasi-Self-Contracted Curves in Complete Geodesic Spaces
In this paper, we introduce the notion of quasi-self-contracted curves (QSC curves for short) in metric spaces. It is a natural generalization of the...
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Hölder continuous weak solutions of the 2D Boussinesq equation with thermal diffusion
We show the existence of Hölder continuous periodic weak solutions of the 2D Boussinesq equation with thermal diffusion which satisfy the prescribed...
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Characterization of Hölder and Sobolev spaces via the continuous wavelet transform with rotations
The continuous wavelet transform with rotations in higher dimensions is used to characterize the Hölder and Sobolev spaces for functions
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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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Universal heavy-ball method for nonconvex optimization under Hölder continuous Hessians
We propose a new first-order method for minimizing nonconvex functions with Lipschitz continuous gradients and Hölder continuous Hessians. The...
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Wellposedness of Viscosity Solutions to Weakly Coupled HJB Equations Under Hölder continuous conditions
We establish the existence and uniqueness of viscosity solutions to the weakly coupled second-order parabolic Hamilton–Jacobi–Bellman equations under...
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Schauder Estimates for Kolmogorov-Fokker-Planck Operators with Coefficients Measurable in Time and Hölder Continuous in Space
We consider degenerate Kolmogorov-Fokker-Planck operators $$\mathcal...
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Geometric Characterizations of Hölder-Continuous Quasi-Distances and Applications
A number of geometric characterizations of Hölder-continuous quasi-distances on a set X are obtained. Such characterizations are then applied to...
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Nonexistence of spectral gaps in Hölder spaces for continuous time dynamical systems
We show that there is a natural restriction on the smoothness of spaces where the transfer operator for a continuous dynamical system has a spectral...
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On boundary Hölder logarithmic continuity of map**s in some domains
We study map**s satisfying some estimate of distortion of modulus of families of paths. Under some conditions on definition and mapped domains, we...
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Existence of Hölder Continuous Solutions for a Class of Degenerate Fourth-Order Elliptic Equations
This paper deals with the existence of bounded and locally Hölder continuous weak solutions of a homogeneous Dirichlet problem related to a class of...
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On Hölder Continuity of Solutions to the Beltrami Equations
We study the problem of local behavior of solutions to the Beltrami equations in arbitrary domains and establish sufficient conditions for the...
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On Logarithmic Hölder Continuity of Map**s on the Boundary
The results of this chapter were obtained together with S. Skvortsov and O. Dovhopiatyi. As is known, quasiconformal map**s and map**s with...
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