Regularity of quasilinear sub-elliptic equations in the Heisenberg group
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Mukherjee, Shirsho; Zhong, Xiao (Mathematical Sciences Publishers, 2021)We study the regularity of minima of scalar variational integrals of p-growth, 1<p><∞, in the Heisenberg group and prove the Hölder continuity of horizontal gradient of minima.</p>
La Manna, Domenico Angelo; Leone, Chiara; Schiattarella, Roberta (Birkhäuser, 2020)In this paper we consider a linear elliptic equation in divergence form ∑i,jDj(aij(x)Diu)=0in Ω. (0.1) Assuming the coefficients aij in W1,n(Ω) with a modulus of continuity satisfying a certain Dini-type continuity ...
Fässler, Katrin; Orponen, Tuomas (Elsevier BV, 2021)Let be the first Heisenberg group, and let be a kernel which is either odd or horizontally odd, and satisfies The simplest examples include certain Riesz-type kernels first considered by Chousionis and Mattila, and the ...
Le Donne, Enrico; Li, Sean; Rajala, Tapio (Oxford University Press; London Mathematical Society, 2017)We show that the Heisenberg group is not minimal in looking down. This answers Problem 11.15 in Fractured fractals and broken dreams by David and Semmes, or equivalently, Question 22 and hence also Question 24 in ...
Chousionis, Vasileios; Fässler, Katrin; Orponen, Tuomas (Johns Hopkins University Press, 2019)The purpose of this paper is to introduce and study some basic concepts of quantitative rectifiability in the first Heisenberg group H. In particular, we aim to demonstrate that new phenomena arise compared to the Euclidean ...