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Zaprta kvazikonveksnost v nelinearni teoriji elastičnosti : magistrsko delo
Jesenko, Martin, 1977-
Obravnavan je problem obstoja minimizatorjev variacijske naloge s predpisanimi robnimi pogoji. Do take naloge nas med drugim privede iskanje stabilnih ravnovesnih položajev hiperelastičnega sredstva. ...Tako je prvo poglavje posvečeno temu področju mehanike. Poleg tega je predstavljena še direktna metoda, na kateri temelji dokazovanje eksistence rešitev. Ker v direktni metodi uporabljamo lastnosti šibke topologije, so potrebna sredstva s tega področja razdelana v drugem poglavju, kjer vpeljemo tudi prostore Soboljeva, ki so zaradi refleksivnosti najbolj primeren prostor dopustnih rešitev. Tretje poglavje nas seznani s kvazikonveksnostjo, ki je potreben pogoj za rešitev naše naloge. Najdaljše, četrto poglavje obravnava problem limitnega prehoda pri šibki konvergenci. Bistveno orodje pri tem so Youngove mere. S poznavanjem lastnosti Youngovih mer v petem poglavju poiščemo zadosten pogoj za obstoj rešitve. To je zaprta kvazikonveksnost.
Type of material - master's thesis
; adult, serious
Publication and manufacture - Ljubljana : [M. Jesenko], 2006
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