Advances in Nonlinear Analysis, 2018 We consider nonlinear sub-elliptic systems with VMO-coefficients in the Heisenberg group and prove partial Hölder continuity results for weak solutions using a generalization of the technique of 𝒜{\mathcal{A}}-harmonic approximation.
Wang Jialin, Manfredi Juan J.
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Hölder continuity of weak solutions to evolution equations with distributed order fractional time derivative [PDF]
Mathematische Annalen, 2023 We study the regularity of weak solutions to evolution equations with distributed order fractional time derivative. We prove a weak Harnack inequality for nonnegative weak supersolutions and Hölder continuity of weak solutions to this problem.
A. Kubica, K. Ryszewska, Rico Zacher
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Boundary Hölder continuity of stable solutions to semilinear elliptic problems in 𝐶1,1 domains [PDF]
Journal für die Reine und Angewandte Mathematik, 2023 This article establishes the boundary Hölder continuity of stable solutions to semilinear elliptic problems in the optimal range of dimensions n ≤ 9 n\leq 9 , for C 1 , 1 C^{1\smash{,}1} domains.
Iñigo U. Erneta
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A perturbative approach to Hölder continuity of solutions to a nonlocal p-parabolic equation [PDF]
Journal of evolution equations (Printed ed.), 2023 We study local boundedness and Hölder continuity of a parabolic equation involving the fractional p-Laplacian of order s, with ...
A. Tavakoli
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Local Hölder continuity for fractional nonlocal equations with general growth [PDF]
Mathematische Annalen, 2021 We study generalized fractional p-Laplacian equations to prove local boundedness and Hölder continuity of weak solutions to such nonlocal problems by finding a suitable fractional Sobolev-Poincaré inquality.
Sun-Sig Byun, Hyojin Kim, J. Ok
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Hölder Continuity and Boundedness Estimates for Nonlinear Fractional Equations in the Heisenberg Group [PDF]
Journal of Geometric Analysis, 2022 We extend the celebrate De Giorgi-Nash-Moser theory to a wide class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional p -Laplacian operator on the Heisenberg-Weyl group $$\mathbb
M. Manfredini +3 more
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The boundedness and Hölder continuity of weak solutions to elliptic equations involving variable exponents and critical growth [PDF]
Journal of Differential Equations, 2020 In this paper we prove the boundedness and Holder continuity of quasilinear elliptic problems involving variable exponents for a homogeneous Dirichlet and a nonhomogeneous Neumann boundary condition, respectively. The novelty of our work is the fact that
Ky Ho +3 more
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Journal of evolution equations (Printed ed.), 2022 We show interior Hölder continuity for a class of quasi-linear degenerate reaction-diffusion equations. The diffusion coefficient in the equation has a porous medium type degeneracy and its primitive has a singularity.
Victor Hissink Muller
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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 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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