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Convexity of power functions and bilinear embedding for divergence-form operators with complex coefficientsCarbonaro, Andrea ; Dragičević, OliverVpeljemo pogoj na akretivne matrične funkcije, imenovan ▫$p$▫-eliptičnost, in obravnavamo njegovo uporabo v ▫$L^p$▫ teoriji eliptičnih parcialnih diferencialnih enačb s kompleksnimi koeficienti. Naši ... primeri so: (i) posplošena konveksnost potenčnih funkcij (Bellmanovih funkcij), (ii) brezdimenzijske bilinearne vložitve, (iii) ▫$L^p$▫ kontraktivnost polgrup in (iv) holomorfni funkcijski račun. Nedavni rezultati Dindoša in Pipher vzpostavljajo tesno vez med ▫$p$▫-eliptičnostjo in (v) regularnostno teorijo eliptičnih parcialnih diferencialnih enačb s kompleksnimi koeficienti. Pogoj ▫$p$▫-eliptičnosti izhaja iz študija enakomerne pozitivnosti kvadratne forme, pridružene obravnavani matriki ter, po drugi strani, Hessejevi matriki potenčne funkcije. Naši rezultati v zvezi s kontraktivnostjo razširijo starejše izreke, ki sta jih dokazala Cialdea in Maz'ya.Source: Journal of the European Mathematical Society. - ISSN 1435-9855 (Vol. 22, iss. 10, 2020, str. 3175-3221)Type of material - article, component part ; adult, seriousPublish date - 2020Language - englishCOBISS.SI-ID - 46804227
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source: Journal of the European Mathematical Society. - ISSN 1435-9855 (Vol. 22, iss. 10, 2020, str. 3175-3221)
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Carbonaro, Andrea | ![]() |
Dragičević, Oliver | 19285 |
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