In this thesis we study semilinear elliptic problems of second and fourth order using some well known functional inequalities, as Hardy-Sobolev inequalities and Trudinger-Moser inequalities. We prove existence and non existence of solutions, regularity of solutions and a priori estimates for solutions.
SOME APPLICATIONS OF FUNCTIONAL INEQUALITIES TO SEMILINEAR ELLIPTIC EQUATIONS / T. Passalacqua ; advisor: B. Ruf ; coordinator: L. Van Geemen. DIPARTIMENTO DI MATEMATICA "FEDERIGO ENRIQUES", 2015 Dec 09. 28. ciclo, Anno Accademico 2015. [10.13130/passalacqua-tommaso_phd2015-12-09].
SOME APPLICATIONS OF FUNCTIONAL INEQUALITIES TO SEMILINEAR ELLIPTIC EQUATIONS
T. Passalacqua
2015
Abstract
In this thesis we study semilinear elliptic problems of second and fourth order using some well known functional inequalities, as Hardy-Sobolev inequalities and Trudinger-Moser inequalities. We prove existence and non existence of solutions, regularity of solutions and a priori estimates for solutions.
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