LEADER 03690nam0 22005173i 450 001 VAN00269009 005 20260703105825.339 017 70$2N$a9781461237365 035 40$a799191402 100 $a20231219d1988 |0itac50 ba 101 $aeng 102 $aUS 105 $a|||| ||||| 181 $ai$b e 182 $ab 183 $acr 200 1 $aBoundary value problems of finite elasticity$elocal theorems on existence, uniqueness, and analytic dependence on data$fTullio Valent 210 $aNew York$cSpringer$d1988 215 $axii, 191 p.$d25 cm 327 $aIn this book I present, in a systematic form, some local theorems on existence, uniqueness, and analytic dependence on the load, which I have recently obtained for some types of boundary value problems of finite elasticity. Actually, these results concern an n-dimensional (n ~ 1) formal generalization of three-dimensional elasticity. Such a generalization, be­ sides being quite spontaneous, allows us to consider a great many inter­ esting mathematical situations, and sometimes allows us to clarify certain aspects of the three-dimensional case. Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality. Note that I concentrate on simultaneous local existence and uniqueness; thus, I do not deal with the more general theory of exis­ tence. Moreover, I restrict my discussion to compressible elastic bodies and I do not treat unilateral problems. The clever use of the inverse function theorem in finite elasticity made by STOPPELLI [1954, 1957a, 1957b], in order to obtain local existence and uniqueness for the traction problem in hyperelasticity under dead loads, inspired many of the ideas which led to this monograph. Chapter I aims to give a very brief introduction to some general concepts in the mathematical theory of elasticity, in order to show how the boundary value problems studied in the sequel arise. Chapter II is very technical; it supplies the framework for all sub­ sequent developments. 410 1$1001VAN00048430$12001 $aSpringer tracts in natural philosophy$1210 $aBerlin [etc.]$cSpringer$d1964-1998.$v31 500 1$3VAN00302674$aBoundary value problems of finite elasticity$9347906 606 $a34Bxx$xBoundary value problems for ordinary differential equations [MSC 2020]$3VANC023485$2MF 606 $a35B30$xDependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs [MSC 2020]$3VANC028997$2MF 606 $a74-XX$xMechanics of deformable solids [MSC 2020]$3VANC022466$2MF 606 $a74B20$xNonlinear elasticity [MSC 2020]$3VANC021528$2MF 610 $aBanach Spaces$9KW:K 610 $aDeformation$9KW:K 610 $aDevelopment$9KW:K 610 $aElasticity$9KW:K 610 $aElastostatics$9KW:K 610 $aImplicit functions$9KW:K 610 $aMaterials$9KW:K 610 $aMeasure$9KW:K 610 $aStatics$9KW:K 620 $aUS$dNew York$3VANL000011 700 1$aValent$bTullio$3VANV039199$041059 712 $aSpringer $3VANV108073$4650 801 $aIT$bSOL$c20260807$gRICA 856 4 $uhttps://doi.org/10.1007/978-1-4612-3736-5$zE-book ? Accesso al full-text attraverso riconoscimento IP di Ateneo, proxy e/o Shibboleth 899 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$1IT-CE0120$2VAN08 912 $fN 912 $aVAN00269009 950 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$d08DLOAD e-book 7873 $e08eMF7873 20231220 996 $aBoundary Value Problems of Finite Elasticity$9347906 997 $aUNICAMPANIA