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14 papers · 2 filters

math.AP2018★ 1 cited

On the supremal version of the Alt-Caffarelli minimization problem

Graziano Crasta, Ilaria Fragalà

This is a companion paper to our recent work [9], where we studied the interior Bernoulli free boundary for the infinity Laplacian. Here we consider its variational side, which cor…

math.AP2018

On the first eigenvalue of the normalized p-Laplacian

Graziano Crasta, Ilaria Fragalà, Bernd Kawohl

We prove that, if is an open bounded domain with smooth and connected boundary, for every the first Dirichlet eigenvalue of the normalized -Laplacian i…

math.AP2018★ 7 cited

Erratum: "On the nonlocal Cahn-Hilliard-Brinkman and Cahn-Hilliard-Hele-Shaw systems" [Comm. Pure Appl. Anal. 15 (2016), 299-317]

Francesco Della Porta, Maurizio Grasselli

In this note, we want to highlight and correct an error in the paper "On the nonlocal Cahn-Hilliard-Brinkman and Cahn-Hilliard-Hele-Shaw systems" [Comm. Pure Appl. Anal. 15 (2016),…

math.AP2018★ 12 cited

Normalized ground states for the NLS equation with combined nonlinearities

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|^{p-2} u \qquad \text{in…

math.AP2018★ 3 cited

Improved Multipolar Poincaré-Hardy inequalities on Cartan-Hadamard Manifolds

Elvise Berchio, Debdip Ganguly, Gabriele Grillo

We prove a family of improved multipolar Poincaré-Hardy inequalities on Cartan-Hadamard manifolds. For suitable configurations of poles, these inequalities yield an improved multip…

math.AP2018★ 12 cited

The gap in Pure Traction Problems between Linear Elasticity and Variational Limit of Finite Elasticity

Francesco Maddalena, Danilo Percivale, Franco Tomarelli

A limit elastic energy for pure traction problem is derived from re-scaled nonlinear energy of an hyperelastic material body subject to an equilibrated force field. We show that th…

math.AP2018★ 12 cited

Analysis of a model of elastic dislocations in geophysics

Andrea Aspri, Elena Beretta, Anna L. Mazzucato +1

We analyze a mathematical model of elastic dislocations with applications to geophysics, where by an elastic dislocation we mean an open, oriented Lipschitz surface in the interior…

math.AP2018

Nonexistence for hyperbolic problems on Riemannian manifolds

Dario D. Monticelli, Fabio Punzo, Marco Squassina

We establish necessary conditions for the existence of solutions to a class of semilinear hyperbolic problems on complete noncompact Riemannian manifolds, extending some nonexisten…

math.AP2018★ 91 cited

Normalized solutions for Nonlinear Schrödinger systems on bounded domains

Benedetta Noris, Hugo Tavares, Gianmaria Verzini

We analyze -normalized solutions of nonlinear Schrödinger systems of Gross-Pitaevskii type, on bounded domains, with homogeneous Dirichlet boundary conditions. We provide suff…

math.AP2018★ 2 cited

Stability properties and dynamics of solutions to viscous conservation laws with mean curvature operator

Raffaele Folino, Maurizio Garrione, Marta Strani

In this paper we study the long time dynamics of the solutions to the initial-boundary value problem for a scalar conservation law with a saturating nonlinear diffusion. After disc…

math.AP2018★ 11 cited

A Minimaxmax Problem for Improving the Torsional Stability of Rectangular Plates

Elvise Berchio, Davide Buoso, Filippo Gazzola +1

We use a gap function in order to compare the torsional performances of different reinforced plates under the action of external forces. Then, we address a shape optimization probl…

math.AP2018★ 18 cited

The nodal set of solutions to some elliptic problems: sublinear equations, and unstable two-phase membrane problem

Nicola Soave, Susanna Terracini

We are concerned with the nodal set of solutions to equations of the form \begin{equation*} -Δu = λ_+ \left(u^+\right)^{q-1} - λ_- \left(u^-\right)^{q-1} \quad \text{in } \end…

math.AP2018★ 4 cited

A transmission problem on a polygonal partition: regularity and shape differentiability

Elena Beretta, Elisa Francini, Sergio Vessella

We consider a transmission problem on a polygonal partition for the two-dimensional conductivity equation. For suitable classes of partitions we establish the exact behaviour of th…

math.AP2018

Optimal distributed control of two-dimensional nonlocal Cahn-Hilliard-Navier-Stokes systems with degenerate mobility and singular potential

S. Frigeri, M. Grasselli, J. Sprekels

In this paper, we consider a two-dimensional diffuse interface model for the phase separation of an incompressible and isothermal binary fluid mixture with matched densities. This…