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National Repository of Grey Literature 12 records found  previous11 - 12  jump to record: Search took 0.01 seconds. 
Sobolev embedding theorem on domains without Lipschitz boundary
 Roskovec, Tomáš ; Hencl, Stanislav (advisor) ; Honzík, Petr (referee)
We study the Sobolev embeddings theorem and formulate modified theorems on domains with nonlipschitz boundary. The Sobolev embeddings the- orem on a domain with Lipschitz boundary claims f ∈ W1,p ⇒ f ∈ Lp∗ (p) , kde p∗ (p) = np n − p . The function p∗ (p) is continuous and even smooth. We construct a domain with nonlipschitz boundary and function of the optimal embedding i.e. analogy of p∗ (p) is not continous. In the first part, according to [1], we construct the domain with the point of discontinuity for p = n = 2. Though we used known construction of domain, we prove this by using more simple and elegant methods. In the second part of thesis we suggest the way how to generalize this model domain and shift the point of discontinuity to other point than p = n = 2.
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Differentiability of the inverse mapping
 Konopecký, František ; Hencl, Stanislav (advisor) ; Honzík, Petr (referee)
Primary objective of the thesis is proof of the statement that if for ∈ ℕ a ≥ 1 a bilipschitz mapping belongs to +1, loc ∩ ,∞ loc then also its inverse −1 belongs to +1, loc . We prove a similar statement also for spaces loc . For this purpose we construct a new ordering of -th partial derivatives to generalized Jacobian matrix. Thanks to this matrix we are able to differentiate matrices in an applicable way. Generalized Jacobian matrix is projected so that there still holds the Chain rule and, in some way, also rules for matrices product differentiation. 1
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