arXiv subjects

Krzysztof Chełmiński

Publications and source records attributed to Krzysztof Chełmiński.

4 recordsLinked to original sources

arXiv2026

Harmonic mappings on Grushin planes, part II

We study harmonic mappings between the source domain in the $α$-Grushin plane and the target domain in the $β$-Grushin plane for $α$ not necessarily equal to $β$ and $α\in [0,1)$. Our harmonic mappings arise as a Euler--Lagrange system of equations related to the Dirichlet energy and are studied in weak and strong forms. The key results enclose the second order regularity of harmonic mappings, the Bochner identity, the weak Harnack estimates for coordinate functions of a harmonic mapping, as well as the Caccioppoli estimates and the Liouville type theorem. Furthermore, we discuss several examples of (Grushin) harmonic mappings and, in particular, relate them to holomorphic mappings in the plane.

math.AP↗

arXiv2015

Renormalised solutions in thermo-visco-plasticity for a Norton-Hoff type model. Part I: the truncated case

We prove existence of global in time strong solutions to the truncated thermo- visco-plasticity with an inelastic constitutive function of Norton-Hoff type. This result is a starting point to obtain renoramlised solutions for the considered model without truncations. The method of our proof is based on Yosida approximation of the maximal monotone term and a passage to the limit.

math.AP↗

arXiv2014

Well-posedness for dislocation based gradient visco-plasticity with isotropic hardening

In this work we establish the well-posedness for infinitesimal dislocation based gradient viscoplasticity with isotropic hardening for general gradient monotone plastic flows. We assume an additive split of the displacement gradient into non-symmetric elastic distortion and non-symmetric plastic distortion. The thermodynamic potential is augmented with a term taking the dislocation density tensor $\operatorname{Curl} p$ into account. The constitutive equations in the models we study are assumed to be of self-controlling type. Based on the generalized version of Korn's inequality for incompatible tensor fields (the non-symmetric plastic distortion) due to Neff/Pauly/Witsch the existence of solutions of quasi-static initial-boundary value problems under consideration is shown using a time-discretization technique and a monotone operator method.

math.AP↗

arXiv2014

A first regularity result for the Armstrong-Frederick cyclic hardening plasticity model with Cosserat effects

The purpose of this article is to prove the Hölder continuity up to the boundary of the displacement vector and the microrotation matrix for the quasistatic, rate-independent Armstrong-Frederick cyclic hardening plasticity model with Cosserat effects. This model is of non-monotone and non-associated type. In the case of two space dimensions we use the hole-filling technique of Widman and the Morrey's Dirichlet growth theorem.

math.AP↗