Université de Fribourg

Intrinsic geometry and analysis of Finsler structures

Guo, Chang-Yu

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.

Université de Fribourg

Fractional Sobolev-Poincaré inequalities in irregular domains

Guo, Chang-Yu

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...

Université de Fribourg

Mappings of finite distortion: boundary extensions in uniform domains

Äkkinen, Tuomo ; Guo, Chang-Yu

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...

Université de Fribourg

Quantitative uniqueness estimates for p-Laplace type equations in the plane

Guo, Chang-Yu ; Kar, Manas

In: Nonlinear Analysis: Theory, Methods & Applications, 2016, vol. 143, p. 19–44