REDUCTION OF DIMENSION AS A CONSEQUENCE OF NORM‐RESOLVENT CONVERGENCE AND APPLICATIONS
David Krejčiřı́kDepartment of MathematicsFaculty of Nuclear Sciences and Physical EngineeringCzech Technical University in PragueTrojanova 1312000Prague 2Czech RepublicNicolas RaymondIRMARUniversité de Rennes 1Campus de BeaulieuF‐35042Rennes cedexFranceJulien RoyerInstitut de Mathématiques de Toulouse UniversitéToulouse 3, 118 route de Narbonne, F‐31062Toulousecedex 9FrancePetr SieglMathematical InstituteUniversity of BernAlpeneggstrasse 223012BernSwitzerland
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Аннотация
This paper is devoted to dimensional reductions via the norm-resolvent convergence. We derive explicit bounds on the resolvent difference as well as spectral asymptotics. The efficiency of our abstract tool is demonstrated by its application on seemingly different partial differential equation problems from various areas of mathematical physics; all are analysed in a unified manner, known results are recovered and new ones established.
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