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Title: Bounded variation solutions of capillarity-type equations
Authors: Rivetti, Sabrina
Supervisore/Tutore: Omari, Pierpaolo
Issue Date: 23-Apr-2014
Publisher: Università degli studi di Trieste
Abstract: We investigate by different techniques, the solvability of a class of capillarity-type problems, in a bounded N-dimensional domain. Since our approach is variational, the natural context where this problem has to be settled is the space of bounded variation functions. Solutions of our equation are defined as subcritical points of the associated action functional.
We first introduce a lower and upper solution method in the space of bounded variation functions. We prove the existence of solutions in the case where the lower solution is smaller than the upper solution. A solution, bracketed by the given lower and upper solutions, is obtained as a local minimizer of the associated functional without any assumption on the boundedness of the right-hand side of the equation. In this context we also prove order stability results for the minimum and the maximum solution lying between the given lower and upper solutions. Next we develop an asymmetric version of the Poincaré inequality in the space of bounded variation functions. Several properties of the curve C are then derived and basically relying on these results, we discuss the solvability of the capillarity-type problem, assuming a suitable control on the interaction of the supremum and the infimum of the function at the right-hand side with the curve C. Non-existence and multiplicity results are investigated as well. The one-dimensional case, which sometimes presents a different behaviour, is also discussed. In particular, we provide an existence result which recovers the case of non-ordered lower and upper solutions.
Ciclo di dottorato: XXV Ciclo
Description: 2012/2013
Keywords: Capillarity equation
BV functions
Variational methods
Nonsmooth critical point theory
Language: en
Type: Doctoral Thesis
Settore scientifico-disciplinare: MAT/05 ANALISI MATEMATICA
NBN: urn:nbn:it:units-12588
Appears in Collections:Scienze matematiche e informatiche

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