In this note we revisit Almgrenâ€™s theory of Q-valued functions, that are functions taking values in the space AQ(R) of unordered Q-tuples of points in R. In particular: â€¢ we give shorter versions ofâ€¦ (More)

We consider general integral functionals on the Sobolev spaces of multiple valued functions introduced by Almgren. We characterize the semicontinuous ones and recover earlier results of Mattila inâ€¦ (More)

We study the asymptotic behavior, as Îµ tends to zero, of the functionals F k Îµ introduced by Coleman and Mizel in the theory of nonlinear second-order materials; i.e., F k Îµ (u) := Ë† I â€ž W (u) Îµ âˆ’ kâ€¦ (More)

We provide new elementary proofs of the following two results: every complex variety is locally the graphs of a Dir-minimizing function, first proved by Almgren [1]; the gradients of Dir-minimizingâ€¦ (More)

In this paper we develop a theory on the higher integrability and the approximation of area-minimizing currents. We prove an a priori estimate on the Lebesgue density of the Excess measure which canâ€¦ (More)

In this paper, we construct global distributional solutions to the volume-preserving mean-curvature flow using a variant of the time-discrete gradient flow approach proposed independently by Almgren,â€¦ (More)

In this paper, we construct global distributional solutions to the volume-preserving mean-curvature flow using a variant of the time-discrete gradient flow approach proposed independently by Almgrenâ€¦ (More)

Spatial distribution of the individuals belonging to different species of the Seslerio-Caricetum sempervirentis in the Dolomites was investigated by means of 16 transects each of 2 metar lenght.â€¦ (More)

In this note we give an estimate of the Minkowski dimension of the set of higher multiplicity points of Almgrenâ€™s Dir-minimizing multiple valued functions, thus improving the previously knownâ€¦ (More)

We prove an epiperimetric inequality for the thin obstacle problem, thus extending the pioneering results by Weiss on the classical obstacle problem (Invent. Math., 138 (1999), no. 1, 23â€“50). Thisâ€¦ (More)