On logarithmic Hölder continuity of mappings on the boundary
Annales Fennici Mathematici, 2022 We study mappings satisfying the so-called inverse Poletsky inequality. Under integrability of the corresponding majorant, it is proved that these mappings are logarithmic Hölder continuous in the neighborhood of the boundary points.
E. Sevost’yanov
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Hölder continuity of tangent cones in RCD(K,N) spaces and applications to nonbranching [PDF]
Geometry & Topology, 2020 In this paper we prove that a metric measure space $(X,d,m)$ satisfying the finite Riemannian curvature-dimension condition ${\sf RCD}(K,N)$ is non-branching and that tangent cones from the same sequence of rescalings are H\"older continuous along the ...
Qintao Deng
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Strong continuity for the 2D Euler equations [PDF]
, 2015 We prove two results of strong continuity with respect to the initial datum for bounded solutions to the Euler equations in vorticity form. The first result provides sequential continuity and holds for a general bounded solution.
Spirito, Stefano +2 more
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Hölder continuity of $\omega$-minimizers of functionals with generalized Orlicz growth [PDF]
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2019 We show local Holder continuity of quasiminimizers of functionals with non-standard (Musielak--Orlicz) growth. Compared with previous results, we cover more general minimizing functionals and need fewer assumptions.
Petteri Harjulehto +2 more
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Hölder continuity of absolutely continuous spectral measure for the extended HARPER’S model [PDF]
Nonlinearity, 2020 We establish sharp results on Hölder continuity of the distribution of the spectral measure for the extended Harper’s model in the absolutely continuous spectrum regime.
Xin Zhao
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Hölder Continuity of the Minimizer of an Obstacle Problem with Generalized Orlicz Growth [PDF]
International mathematics research notices, 2020 We prove local $C^{0,\alpha }$- and $C^{1,\alpha }$-regularity for the local solution to an obstacle problem with nonstandard growth. These results cover as special cases standard, variable exponent, double phase, and Orlicz growth.
Arttu Karppinen, Mikyoung Lee
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Hölder Continuity for the Parabolic Anderson Model with Space-Time Homogeneous Gaussian Noise [PDF]
Acta Mathematica Scientia, 2018 In this article, we consider the Parabolic Anderson Model with constant initial condition, driven by a space-time homogeneous Gaussian noise, with general covariance function in time and spatial spectral measure satisfying Dalang’s condition.
R. Balan +2 more
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Joint Hölder Continuity of Parabolic Anderson Model [PDF]
Acta Mathematica Scientia, 2018 We obtain the Holder continuity and joint Hölder continuity in space and time for the random field solution to the parabolic Anderson equation $$(\partial_t-\frac{1}{2}\Delta)u=u\diamond\dot{W}$$(∂t−12Δ)u=u⋄W˙ in d-dimensional space, where Ẇ is a mean ...
Yaozhong Hu, Khoa Le
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Hölder Continuity for a Family of Nonlocal Hypoelliptic Kinetic Equations [PDF]
SIAM Journal on Mathematical Analysis, 2018 In this work, Holder continuity is obtained for solutions to the nonlocal kinetic Fokker-Planck Equation, and to a family of related equations with general integro-differential operators.
L. Stokols
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On the Hölder continuity of weak solutions to nonlinear parabolic systems in two space dimensions [PDF]
, 1998 summary:We prove the interior Hölder continuity of weak solutions to parabolic systems $$ \frac{\partial u^j}{\partial t}-D_\alpha a_j^\alpha(x,t,u,\nabla u)=0 \text{ in } Q \quad (j=1,\ldots,N) $$ ($Q=\Omega\times(0,T),\Omega\subset\Bbb R^2$), where ...
Naumann, J., Wolff, M., Wolf, J.
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