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math.AP2019★ 11 cited

Integral representation of local left--invariant functionals in Carnot groups

Alberto Maione, Eugenio Vecchi

The aim of this note is to prove a representation theorem for left--invariant functionals in Carnot groups. As a direct consequence, we can also provide a -convergence result fo…

math.AP2019★ 17 cited

Nonzero positive solutions of elliptic systems with gradient dependence and functional BCs

Stefano Biagi, Alessandro Calamai, Gennaro Infante

We discuss, by topological methods, the solvability of systems of second-order elliptic differential equations subject to functional boundary conditions under the presence of gradi…

math.AP2019★ 3 cited

The stochastic Cahn-Hilliard equation with degenerate mobility and logarithmic potential

Luca Scarpa

We prove existence of martingale solutions for the stochastic Cahn-Hilliard equation with degenerate mobility and multiplicative Wiener noise. The potential is allowed to be of log…

math.AP2019★ 7 cited

On unique continuation principles for some elliptic systems

Ederson Moreira dos Santos, Gabrielle Nornberg, Nicola Soave

In this paper we prove unique continuation principles for some systems of elliptic partial differential equations satisfying a suitable superlinearity condition. As an application,…

math.AP2019★ 4 cited

On the determination of ischemic regions in the monodomain model of cardiac electrophysiology from boundary measurements

Elena Beretta, Cecilia Cavaterra, Luca Ratti

In this paper we consider the monodomain model of cardiac electrophysiology. After an analysis of the well-posedness of the model, we determine an asymptotic expansion of the pertu…

math.AP2019★ 10 cited

The Brunn-Minkowski inequality for the principal eigenvalue of fully nonlinear homogeneous elliptic operators

Graziano Crasta, Ilaria Fragalà

We prove that the principal eigenvalue of any fully nonlinear homogeneous elliptic operator which fulfills a very simple convexity assumption satisfies a Brunn-Minkowski type inequ…

math.AP2019★ 11 cited

Normalized ground states for the NLS equation with combined nonlinearities: the Sobolev critical case

Nicola Soave

We study existence and properties of ground states for the nonlinear Schrödinger equation with combined power nonlinearities \[ -Δu= λu + μ|u|^{q-2} u + |u|^{2^*-2} u \qquad \text{…