University of Jyväskylä

Dissertation: 29.11 Mappings of finite distortion: mappings in the Sobolev space W1,n-1 with integrable inner distortion (Tengvall)

Start date: Nov 29, 2014 12:00 AM

End date: Nov 29, 2014 03:00 PM

Location: Seminaarinmäki, H320

Ville Tengvall. Kuvaaja: Marie HolmstedtM.Sc. Ville Tengvall defends his doctoral dissertation in Mathematics. Opponent professori Peter Hästö (Oulun yliopisto/Turun yliopisto) and custos Professor Tero Kilpeläinen (University of Jyväskylä). The even is in Finnish.

Abstract

The area of this thesis is Geometric function theory. We will study deformations of physical objects in the Euclidean spaces in terms of mappings of finite distortion. We will study differentiability of

these deformations and also regularity of the inverse. Moreover, we will discuss the geometric foundation that has been created to study mappings of finite distortion, and give some new aspects to this study as well.

The thesis consists of three articles. In the first article we give sufficient topological and conformal conditions which guarantee mappings in the Sobolev space W1,n-1 to be differentiable almost everywhere. In the second article we give sufficient topological and geometrical conditions which guarantee these mappings to have finite distortion up to a sign of the Jacobian. In the third article we study regularity of the inverse mapping in terms of the outer distortion function. Especially, we will expose the exponent gap for the logarithmic modulus of continuity of the inverse mapping when the outer distortion function reaches certain critical integrability class.

  • Further information:

Ville Tengvall, tel. +358 40 824 3702, ville.tengvall@jyu.fi

Communications officer Anitta Kananen, tel. +358 40 805 4142, tiedotus@jyu.fi