Title: Gradient mapping of functions of several variables Author: Alena Skálová Department: Department of Mathematical Analysis Supervisor: doc. RNDr. Miroslav Zelený, Ph.D., Department of Mathematical Analysis Abstract: In the thesis we prove that the following statement holds true. For each d ≥ 2, for each open bounded set U ⊂ Rd and for each set F ⊂ Rd of the Borel class Fσ there exists an everywhere differentiable function u: Rd → R such that ∇u(x) ∈ U for all x ∈ Rd , ∇u(x) ∈ U for all x ∈ F, ∇u(x) ∈ ∂U for λd-almost all x ∈ Rd \ F.
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:335101 |
| Date | January 2014 |
| Creators | Skálová, Alena |
| Contributors | Zelený, Miroslav, Holický, Petr |
| Source Sets | Czech ETDs |
| Language | Czech |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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