Hölder continuity for sub-elliptic systems under the sub-quadratic controllable growth in Carnot groups

Jialin Wang; Dongni Liao; Zefeng Yu

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Displaying similar documents to “Hölder continuity for sub-elliptic systems under the sub-quadratic controllable growth in Carnot groups”

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Ye-Lin Ou (1997)

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We introduce O-systems (Definition 3.1) of orthogonal transformations of $ℝ^{m}$ , and establish $ℝ$ correspondences both between equivalence classes of Clifford systems and those of O-systems, and between O-systems and orthogonal multiplications of the form $μ : ℝ^{n} \times ℝ^{m} \to ℝ^{m}$ , which allow us to solve the existence problems both for $O$ -systems and for umbilical quadratic harmonic morphisms simultaneously. The existence problem for general quadratic harmonic morphisms is then solved by the Splitting Lemma. We also...

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This paper is concerned with strong solutions of uniformly elliptic equations of non-divergence type in the plane. First, we use the notion of quasiregular gradient mappings to improve Morrey’s theorem on the Hölder continuity of gradients of solutions. Then we show that the Gilbarg-Serrin equation does not produce the optimal Hölder exponent in the considered class of equations. Finally, we propose a conjecture for the best possible exponent and prove it under an additional restriction. ...

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We consider a function which is a viscosity solution of a uniformly elliptic equation only at those points where the gradient is large. We prove that the Hölder estimates and the Harnack inequality, as in the theory of Krylov and Safonov, apply to these functions.