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	Elliptic systems with anisotropic potential: existence and regularity of solutions Peltan, Libor ; Kaplický, Petr (advisor) ; Bulíček, Miroslav (referee) We briefly summarize existing result in theory of minimizers of elliptic variational functionals. We introduce proof of existence and regularity such functional under assumpti- ons of quaziconvexity and izotrophic growth estimates, and discuss possible generalization to anizotropic case. Our proof is a compilation from more sources, modified in order of simplicity, readability and detailed analysis of all steps. Detailed record
	Monotonicity of functions which can be expressed using elementary functions Peltan, Libor ; Bárta, Tomáš (advisor) ; Pyrih, Pavel (referee) For certain types of functions expressible with formula (equivalently: functions from classes closed to arithmetic operations) under stated assumptions, we prove monotonicity at some neighbourhood of +∞. They are: formulas containing exp, log, sin, arctan, etc. with constrainted domain of these functions; power series with cofinite many coefficients positive; various classes of functions expressible with formulas with the requirement of preserving monotony in summation, or multiplication, or the monotony resulting from having a finite number of zero points; and finally formulas with square root. 1 Detailed record
	Elliptic systems with anisotropic potential: existence and regularity of solutions Peltan, Libor ; Kaplický, Petr (advisor) ; Bulíček, Miroslav (referee) We briefly summarize existing result in theory of minimizers of elliptic variational functionals. We introduce proof of existence and regularity such functional under assumpti- ons of quaziconvexity and izotrophic growth estimates, and discuss possible generalization to anizotropic case. Our proof is a compilation from more sources, modified in order of simplicity, readability and detailed analysis of all steps. Detailed record
	Monotonicity of functions which can be expressed using elementary functions Peltan, Libor ; Bárta, Tomáš (advisor) ; Pyrih, Pavel (referee) For certain types of functions expressible with formula (equivalently: functions from classes closed to arithmetic operations) under stated assumptions, we prove monotonicity at some neighbourhood of +∞. They are: formulas containing exp, log, sin, arctan, etc. with constrainted domain of these functions; power series with cofinite many coefficients positive; various classes of functions expressible with formulas with the requirement of preserving monotony in summation, or multiplication, or the monotony resulting from having a finite number of zero points; and finally formulas with square root. 1 Detailed record

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