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  • Uvažujeme obecný nelineární operátor druhého řádu v divergentním tvaru. Nejdříve se tento operátor definuje na Sobolevově prostoru funkcí jedné proměnné a jsou prezentovány nutné a postačující podmínky zaručující jeho monotonii a to jak v obecném, tak v konkrétním případě. Dále jsou tyto výsledky rozšířeny do více prostorových dimenzí. Důsledkem je důkaz nemonotonie stacionárního nelineárního operátoru vedení tepla v libovolné dimenzi. (cs)
  • A general nonlinear elliptic operator of second order in divergence form is considered. First, the operator is defined on a Sobolev space of functions of one variable, and necessary as well as sufficient conditions ensuring the monotony of the operator are given for both general and particular settings. Next, these results are extended into more spatial dimensions. As a consequence, the nonmonotony of a stationary nonlinear heat conduction operator is proven in an arbitrary spatial dimension.
  • A general nonlinear elliptic operator of second order in divergence form is considered. First, the operator is defined on a Sobolev space of functions of one variable, and necessary as well as sufficient conditions ensuring the monotony of the operator are given for both general and particular settings. Next, these results are extended into more spatial dimensions. As a consequence, the nonmonotony of a stationary nonlinear heat conduction operator is proven in an arbitrary spatial dimension. (en)
Title
  • On the Nonmonotony of Nonlinear Elliptic Operators in Divergence Form
  • O nemonotonii nelineárního eleiptického operátoru v divergentním tvaru (cs)
  • On the Nonmonotony of Nonlinear Elliptic Operators in Divergence Form (en)
skos:prefLabel
  • On the Nonmonotony of Nonlinear Elliptic Operators in Divergence Form
  • O nemonotonii nelineárního eleiptického operátoru v divergentním tvaru (cs)
  • On the Nonmonotony of Nonlinear Elliptic Operators in Divergence Form (en)
skos:notation
  • RIV/67985840:_____/04:00022967!RIV06-AV0-67985840
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  • 25;33
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  • P(IAA1019201), Z(AV0Z1019905)
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  • 1
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  • 577905
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  • RIV/67985840:_____/04:00022967
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  • nonlinear elliptic operator; divergence form; monotony (en)
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  • JP - Japonsko
http://linked.open...ontrolniKodProRIV
  • [0C25BAE063D5]
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  • Advances in Mathematical Sciences and Applications
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  • 14
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  • Vejchodský, Tomáš
http://linked.open...n/vavai/riv/zamer
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  • 1343-4373
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