This thesis is devoted to the study of different types of elliptic differential inclusions and their applications to a wide range of implicit equations. We first introduce some general definitions and properties of set-valued analysis, the basic notions of lower semicontinuous multifunction with decomposable values and selection, in particular we make use of the Kuratowski and Ryll-Nardzewski Theorem and the Bressan-Colombo-Fryszkowski Theorem. Then, we investigate some p-Laplacian differential inclusions with a right hand-side both lower semicontinuous and upper semicontinuous in order to show some applications to implicit differential equations. Moreover, we present a different approach to differential inclusions, based on variational methods and locally Lipschitz continuous functions.
Elliptic differential inclusions and applications to implicit equations / Paratore, Andrea. - (2018 Nov 29).
Elliptic differential inclusions and applications to implicit equations
PARATORE, ANDREA
2018-11-29
Abstract
This thesis is devoted to the study of different types of elliptic differential inclusions and their applications to a wide range of implicit equations. We first introduce some general definitions and properties of set-valued analysis, the basic notions of lower semicontinuous multifunction with decomposable values and selection, in particular we make use of the Kuratowski and Ryll-Nardzewski Theorem and the Bressan-Colombo-Fryszkowski Theorem. Then, we investigate some p-Laplacian differential inclusions with a right hand-side both lower semicontinuous and upper semicontinuous in order to show some applications to implicit differential equations. Moreover, we present a different approach to differential inclusions, based on variational methods and locally Lipschitz continuous functions.File | Dimensione | Formato | |
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