In: Annali di Matematica Pura ed Applicata (1923 -), 2019, vol. 198, no. 2, p. 367–380
We prove local Hölder continuity of quasi-n-harmonic mappings from Euclidean domains into metric spaces with non-positive curvature in the sense of Alexandrov. We also obtain global Hölder continuity of such mappings from bounded Lipschitz domains.
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In: Annali di Matematica Pura ed Applicata (1923 -), 2017, vol. 196, no. 5, p. 1685–1693
In this short note, we prove that if F is a weak upper semicontinuous admissible Finsler structure on a domain in Rn,n≥2Rn,n≥2\mathbb {R}^n, n\ge 2, then the intrinsic distance and differential structures coincide.
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In: Chinese Annals of Mathematics, Series B, 2017, vol. 38, no. 3, p. 839–856
This paper is devoted to the study of fractional (q, p)-Sobolev-Poincaré in- equalities in irregular domains. In particular, the author establishes (essentially) sharp fractional (q, p)-Sobolev-Poincaré inequalities in s-John domains and in domains satisfying the quasihyperbolic boundary conditions. When the order of the fractional derivative tends to 1, our results tend to the results for...
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In: Annali di Matematica Pura ed Applicata (1923 -), 2017, vol. 196, no. 1, p. 65–83
In this paper, we consider mappings on uniform domains with exponentially integrable distortion whose Jacobian determinants are integrable. We show that such mappings can be extended to the boundary, and moreover, these extensions are exponentially integrable with quantitative bounds. This extends previous results of Chang and Marshall (Am J Math 107(5):1015–1033, 1985) on analytic...
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In: Nonlinear Analysis: Theory, Methods & Applications, 2016, vol. 143, p. 19–44
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