We present a series of recent results on some new classes of free boundary problems. Differently from the classical literature, the problems considered have either a "nonlocal" feature (e.g., the interaction or/and the interfacial energy may depend on global quantities) or a "nonlinear" flavor (namely, the total energy is the nonlinear superposition of energy components, thus losing the standard additivity and scale invariances of the problem). The complete proofs and the full details of the results presented here are given in [17, 31, 35, 26, 28, 39].

New trends in free boundary problems / S. Dipierro, A. Karakhanyan, E. Valdinoci. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - 17:2(2017 May), pp. 319-332.

New trends in free boundary problems

S. Dipierro
Primo
;
E. Valdinoci
Ultimo
2017

Abstract

We present a series of recent results on some new classes of free boundary problems. Differently from the classical literature, the problems considered have either a "nonlocal" feature (e.g., the interaction or/and the interfacial energy may depend on global quantities) or a "nonlinear" flavor (namely, the total energy is the nonlinear superposition of energy components, thus losing the standard additivity and scale invariances of the problem). The complete proofs and the full details of the results presented here are given in [17, 31, 35, 26, 28, 39].
free boundary conditions; free boundary problems; instability; nonlocal equations; regularity theory; scaling properties; statistical and nonlinear physics; mathematics (all)
Settore MAT/05 - Analisi Matematica
mag-2017
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/505153
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