Search for dissertations about: "Lukáš Malý"
Found 3 swedish dissertations containing the words Lukáš Malý.
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1. Newtonian Spaces Based on Quasi-Banach Function Lattices
Abstract : The traditional first-order analysis in Euclidean spaces relies on the Sobolev spaces W1,p(Ω), where Ω ⊂ Rn is open and p ∈ [1, ∞].The Sobolev norm is then defined as the sum of Lp norms of a function and its distributional gradient.We generalize the notion of Sobolev spaces in two different ways. READ MORE
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2. Sobolev-Type Spaces : Properties of Newtonian Functions Based on Quasi-Banach Function Lattices in Metric Spaces
Abstract : This thesis consists of four papers and focuses on function spaces related to first-order analysis in abstract metric measure spaces. The classical (i.e., Sobolev) theory in Euclidean spaces makes use of summability of distributional gradients, whose definition depends on the linear structure of Rn. READ MORE
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3. Inverse Problems for Tumour Growth Models and Neural ODEs
Abstract : This thesis concerns the application of methods and techniques from the theory of inverse problems and differential equations to study models arising in the areas of mathematical oncology and deep learning. The first problem studied is to develop methods to perform numerical simulations with full 3-dimensional brain imaging data of reaction-diffusion models for tumour growth forwards as well as backwards in time with the goal of enabling the numerical reconstruction of the source of the tumour given an image (or similar data) at a later stage in time of the tumour. READ MORE