Diseguaglianze di Sobolev sulle ipersuperfici minimali
Una maggiorazione integrale per le curvature delle ipersuperfici minimali
Diseguaglianze isoperimetriche e diseguaglianze di Sobolev
Sulla variazione totale del gradiente di una funzione
Maximum principles and minimal surfaces
Superficie minime illimitate
Sul minimo dell'integrale del gradiente di una funzione
Distribuzioni aventi derivate misure insiemi di perimetro localmente finito
Superfici cartesiane generalizzate ed insiemi di perimetro localmente finito sui prodotti cartesiani
Sul minimo dell'integrale del gradiente di una funzione
Un teorema di esistenza e unicità per il problema dell’area minima in variabili
Sulle singolarità eliminabili delle soluzioni dell'equazione delle superficie minime
Gradient estimates and Harnack inequalities for solutions to the minimal surface equation
A gradient estimate for solutions to the minimal surface equation can be proved by Partial Differential Equations methods, as in [2]. In such a case, the oscillation of the solution controls its gradient. In the article presented here, the estimate is derived from the Harnack type inequality established in [1]. In our case, the gradient is controlled by the area of the graph of the solution or by the integral of it. These new results are similar to the one announced by Ennio De Giorgi in [3].
Caccioppoli sets
The story of the theory of Caccioppoli sets is presented, together with some information about Renato Caccioppoli’s life. The fundamental contributions of Ennio De Giorgi to the theory of Caccioppoli sets are sketched. A list of applications of Cacciopoli sets to the calculus of variations is finally included.
Lagrange multipliers and geometric measure theory
The Bernstein Theorem in Higher Dimensions
In this work we have reconsidered the famous paper of Bombieri, De Giorgi and Giusti [4] and, thanks to the software Mathematica we made it possible for anybody to control the difficult computations.
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