107 citations · 382 across the 27 of their papers we have counts for
34 papers
Spectral partition problems with volume and inclusion constraints
Pêdra D. S. Andrade, Ederson Moreira dos Santos, Makson S. Santos +1
In this paper, we discuss a class of spectral partition problems with a measure constraint, for partitions of a given bounded connected open set. We establish the existence of an o…
Classification and stability of positive solutions to the NLS equation on the -metric graph
Francisco Agostinho, Simão Correia, Hugo Tavares
Given and , we present a complete classification of the positive -solutions of the equation on the -metric graph (consisting of tw…
Optimal uniform bounds for competing variational elliptic systems with variable coefficients
Manuel Dias, Hugo Tavares
Let be an open set. In this work we consider solutions of the following gradient elliptic system \[ -\text{div}(A(x)\nabla u_{i,β}) = f_i(x,u_{i,β}) + a(x)β…
Least energy positive solutions of critical Schrödinger systems with mixed competition and cooperation terms: the higher dimensional case
Hugo Tavares, Song You, Wenming Zou
Let be a smooth bounded domain. In this paper we investigate the existence of least energy positive solutions to the following Schrödinger system with $d\…
Free boundary problems with long-range interactions: uniform Lipschitz estimates in the radius
Nicola Soave, Hugo Tavares, Alessandro Zilio
Consider the class of optimal partition problems with long range interactions \[ \inf \left\{ \sum_{i=1}^k λ_1(ω_i):\ (ω_1,\ldots, ω_k) \in \mathcal{P}_r(Ω) \right\}, \] where $λ_1…
Yamabe systems, optimal partitions, and nodal solutions to the Yamabe equation
Mónica Clapp, Angela Pistoia, Hugo Tavares
We give conditions for the existence of regular optimal partitions, with an arbitrary number of components, for the Yamabe equation on a closed Riemannian manifold $(M…
On the least-energy solutions of the pure Neumann Lane-Emden equation
Alberto Saldaña, Hugo Tavares
We study the pure Neumann Lane-Emden problem in a bounded domain \[ -Δu = |u|^{p-1} u \text{ in }Ω, \qquad \partial_νu=0 \text{ on }\partial Ω, \] in the subcritical, critical, and…
Principal spectral curves for Lane-Emden fully nonlinear type systems and applications
Ederson Moreira dos Santos, Gabrielle Nornberg, Delia Schiera +1
In this paper we exploit the phenomenon of two principal half eigenvalues in the context of fully nonlinear Lane-Emden type systems with possibly unbounded coefficients and weights…
Nodal Solutions for sublinear-type problems with Dirichlet boundary conditions
Denis Bonheure, Ederson Moreira dos Santos, Enea Parini +2
We consider nonlinear second order elliptic problems of the type \[ -Δu=f(u) \text{ in } Ω, \qquad u=0 \text{ on } \partial Ω, \] where is an open -domain in $\mathbb{…
Regularity of all minimizers of a class of spectral partition problems
Hugo Tavares, Alessandro Zilio
We study a rather broad class of optimal partition problems with respect to monotone and coercive functional costs that involve the Dirichlet eigenvalues of the partitions. We show…
Existence of least energy positive solutions to Schrödinger systems with mixed competition and cooperation terms: the critical case
Hugo Tavares, Song You
In this paper we investigate the existence of solutions to the following Schrödinger system in the critical case \begin{equation*} -Δu_{i}+λ_{i}u_{i}=u_{i}\sum_{j = 1}^{d}β_{ij}u_{…
A fountain of positive Bubbles on a Coron's Problem for a Competitive Weakly Coupled Gradient System
Angela Pistoia, Nicola Soave, Hugo Tavares
We consider the following critical elliptic system: \begin{equation*} \begin{cases} -Δu_i=μ_i u_i^{3}+βu_i^{ } \sum\limits_{j\neq i} u_j^{2} \quad \hbox{in}\ Ω_\varepsilon \\ u_i=0…
Bose fluids and positive solutions to weakly coupled systems with critical growth in dimension two
Daniele Cassani, Hugo Tavares, Jianjun Zhang
We prove, using variational methods, the existence in dimension two of positive vector ground states solutions for the Bose-Einstein type systems \begin{equation} \begin{cases} -Δu…
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…
Sharp concentration estimates near criticality for radial sign-changing solutions of Dirichlet and Neumann problems
Massimo Grossi, Alberto Saldaña, Hugo Tavares
We consider radial solutions of the slightly subcritical problem either on () or…
Least energy nodal solutions of Hamiltonian elliptic systems with Neumann boundary conditions
Alberto Saldaña, Hugo Tavares
We study existence, regularity, and qualitative properties of solutions to the system \[ -Δu = |v|^{q-1} v\quad \text{ in }Ω,\qquad -Δv = |u|^{p-1} u\quad \text{ in }Ω,\qquad \part…
Variational problems with long-range interaction
Nicola Soave, Hugo Tavares, Susanna Terracini +1
We consider a class of variational problems for densities that repel each other at distance. Typical examples are given by the Dirichlet functional and the Rayleigh functional \[ D…
Paths to uniqueness of critical points and applications to partial differential equations
Denis Bonheure, Juraj Földes, Ederson Moreira dos Santos +2
We prove a unified and general criterion for the uniqueness of critical points of a functional in the presence of constraints such as positivity, boundedness, or fixed mass. Our me…
On a coupled system of a Ginzburg-Landau equation with a quasilinear conservation law
João-Paulo Dias, Filipe Oliveira, Hugo Tavares
We study the Cauchy problem for a coupled system of a complex Ginzburg-Landau equation with a quasilinear conservation law $$ \left\{\begin{array}{rlll} e^{-iθ}u_t&=&u_{xx}-|u|^2u-…
Spiked solutions for Schrödinger systems with Sobolev critical exponent: the cases of competitive and weakly cooperative interactions
Angela Pistoia, Hugo Tavares
In this paper we deal with the nonlinear Schrödinger system \[ -Δu_i =μ_i u_i^3 + βu_i \sum_{j\neq i} u_j^2 + λ_i u_i, \qquad u_1,\ldots, u_m\in H^1_0(Ω) \] in dimension 4, a probl…
Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with equations
Simão Correia, Filipe Oliveira, Hugo Tavares
In this work we consider the weakly coupled Schrödinger cubic system \[ \begin{cases} \displaystyle -Δu_i+λ_i u_i= μ_i u_i^{3}+ u_i\sum_{j\neq i}b_{ij} u_j^2 \\ u_i\in H^1(\mathbb{…
Dividing the circle
Pedro J. Freitas, Hugo Tavares
There are known constructions for some regular polygons, usually inscribed in a circle, but not for all polygons - the Gauss-Wantzel Theorem states precisely which ones can be cons…
Hölder bounds and regularity of emerging free boundaries for strongly competing Schrödinger equations with nontrivial grouping
Nicola Soave, Hugo Tavares, Susanna Terracini +1
We study regularity issues for systems of elliptic equations of the type \[ -Δu_i=f_{i,β}(x)-β\sum_{j\neq i} a_{ij} u_i |u_i|^{p-1}|u_j|^{p+1} \] set in domains $Ω\subset \mathbb{R…
Ground States for a nonlinear Schrödinger system with sublinear coupling terms
Filipe Oliveira, Hugo Tavares
We study the existence of ground states for the coupled Schrödinger system \begin{equation} \left\{\begin{array}{lll} \displaystyle -Δu_i+λ_i u_i= μ_i |u_i|^{2q-2}u_i+\sum_{j\neq i…