Function spaces and pseudo-differential operators on vector bundles
Authors
Date
2019Copyright
This publication is copyrighted. You may download, display and print it for Your own personal use. Commercial use is prohibited.
The objective of this Master thesis is to give coordinate-free definitions of certain concepts in modern analysis on vector bundles and to apply these tools to elliptic partial differential equations. Topics that we cover are distribution theory, Sobolev spaces and pseudo-differential operators.
Keywords
Metadata
Show full item recordCollections
- Pro gradu -tutkielmat [29052]
Related items
Showing items with similar title or keywords.
-
Generalized finite difference schemes with higher order Whitney forms
Kettunen, Lauri; Lohi, Jonni; Räbinä, Jukka; Mönkölä, Sanna; Rossi, Tuomo (EDP Sciences, 2021)Finite difference kind of schemes are popular in approximating wave propagation problems in finite dimensional spaces. While Yee’s original paper on the finite difference method is already from the sixties, mathematically ... -
Ricci-flow based conformal mapping of the proximal femur to identify exercise loading effects
Narra, Nathaniel; Abe, Shinya; Dimitrov, Vassil; Nikander, Riku; Kouhia, Reijo; Sievänen, Harri; Hyttinen, Jari (Nature Publishing Group, 2018)The causal relationship between habitual loading and adaptive response in bone morphology is commonly explored by analysing the spatial distribution of mechanically relevant features. In this study, 3D distribution of ... -
Quasi-Continuous Vector Fields on RCD Spaces
Debin, Clément; Gigli, Nicola; Pasqualetto, Enrico (Springer, 2021)In the existing language for tensor calculus on RCD spaces, tensor fields are only defined m-a.e.. In this paper we introduce the concept of tensor field defined ‘2-capacity-a.e.’ and discuss in which sense Sobolev vector ... -
Open-source QCD analysis of nuclear parton distribution functions at NLO and NNLO
Walt, Marina; Helenius, Ilkka; Vogelsang, Werner (American Physical Society, 2019)We present new sets of nuclear parton distribution functions (nPDFs) at next-to-leading order and next-to-next-to-leading order. Our analyses are based on deeply inelastic scattering data with charged-lepton and neutrino ... -
Pestov identities and X-ray tomography on manifolds of low regularity
Ilmavirta, Joonas; Kykkänen, Antti (American Institute of Mathematical Sciences (AIMS), 2023)We prove that the geodesic X-ray transform is injective on scalar functions and (solenoidally) on one-forms on simple Riemannian manifolds (M, g) with g ∈ C1,1. In addition to a proof, we produce a redefinition of simplicity ...