P. M. Girão

activity

20142023

most citedConvergence of a crystalline algorithm for the heat equation in one dimension and for the motion of a graph by weighted curvature

59 citations · 382 across the 19 of their papers we have counts for

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Showing 2014Show all

16 papers · 1 filter

math.AP2014

A family of sharp inequalities for Sobolev functions

Pedro M. Girão

Let $N \geq 5$ , $Ω$ be a smooth bounded domain in $R^{N}$ , $2^{*} = \frac{2 N}{N - 2}$ , $a > 0$ , $S=\inf\left\{\left. \int_{\mathbb{R}^{N}}|\nabla u|^2\,\right|\,u\in L^{2^*}(\mat…

math.AP2014★ 5 cited

A sharp inequality for Sobolev functions

Pedro M. Girão

Let $N \geq 5$ , $a > 0$ , $Ω$ be a smooth bounded domain in $R^{N}$ , $2^{*} = \frac{2 N}{N - 2}$ , $2^{#} = \frac{2 ( N - 1 )}{N - 2}$ and $∣∣ u ∣ ∣^{2} = ∣\nabla u ∣_{2}^{2} + a ∣ u ∣_{2}^{2}$ . We prove there…

math.AP2014★ 9 cited

Existence and nonexistence of least energy solutions of the Neumann problem for a semilinear elliptic equation with critical Sobolev exponent and a critical lower-order perturbation

David G. Costa, Pedro M. Girão

Let $Ω$ be a smooth bounded domain in $R^{N}$ , with $N \geq 5$ , $a > 0$ , $α \geq 0$ and $2^{*} = \frac{2 N}{N - 2}$ . We show that the the exponent $q = \frac{2 ( N - 1 )}{N - 2}$ plays a crit…

math.AP2014

Sign changing solutions for elliptic equations with critical growth in cylinder type domains

Pedro M. Girão, Miguel Ramos

We prove the existence of positive and of nodal solutions for $- Δ u = ∣ u ∣^{p - 2} u + μ ∣ u ∣^{q - 2} u$ , $u \in H_{0}^{1} (Ω)$ , where $μ > 0$ and $2 < q < p = 2 N (N - 2)$ , for a class of open subsets $Ω…

math.NA2014★ 59 cited

Convergence of a crystalline algorithm for the motion of a simple closed convex curve by weighted curvature

Pedro M. Girão

Motion by weighted mean curvature is a geometric evolution law for surfaces and represents steepest descent with respect to anisotropic surface energy. It has been proposed that th…

math.NA2014★ 59 cited

Convergence of a crystalline algorithm for the heat equation in one dimension and for the motion of a graph by weighted curvature

Pedro M. Girão, Robert V. Kohn

Motion by (weighted) mean curvature is a geometric evolution law for surfaces, representing steepest descent with respect to (an)isotropic surface energy. It has been proposed that…

math.AP2014★ 2 cited

Multibump nodal solutions for an indefinite nonhomogeneous elliptic problem

Pedro M. Girão, José Maria Gomes

We construct multibump nodal solutions of the elliptic equation $- Δ u = a^{+} [λ u + f (\cdot, u)] - μ a^{-} g (\cdot, u)$ in $H_{0}^{1} (Ω)$ , when $μ$ is large, under appropriate assump…

math.AP2014★ 24 cited

Multibump nodal solutions for an indefinite superlinear elliptic problem

Pedro M. Girão, José Maria Gomes

We define some Nehari-type constraints using an orthogonal decomposition of the Sobolev space $H_{0}^{1}$ and prove the existence of multibump nodal solutions for an indefinite superli…

math.AP2014★ 23 cited

The shape of extremal functions for Poincaré-Sobolev-type inequalities in a ball

Pedro M. Girão, Tobias Weth

We study extremal functions for a family of Poincaré-Sobolev-type inequalities. These functions minimize, for subcritical or critical $p \geq 2$ , the quotient ${\|\nabla u\|_2}/{\|u…

math.AP2014★ 21 cited

Positive solutions to logistic type equations with harvesting

Pedro M. Girão, Hossein Tehrani

We use comparison principles, variational arguments and a truncation method to obtain positive solutions to logistic type equations with harvesting both in $R^{N}$ and in a…

math.AP2014

On the Fučik spectrum of the wave operator and an asymptotically linear problem

Pedro M. Girão, Hossein Tehrani

We study generalized solutions of the nonlinear wave equation $u_{tt} - u_{ss} = a u^{+} - b u^{-} + p (s, t, u),$ with periodic conditions in $t$ and homogeneous Dirichlet conditions in $s$ , und…

math.AP2014★ 3 cited

Bifurcation curves of a diffusive logistic equation with harvesting orthogonal to the first eigenfunction

Pedro M. Girão, Mayte Pérez-Llanos

We study the global bifurcation curves of a diffusive logistic equation, when harvesting is orthogonal to the first eigenfunction of the Laplacian, for values of the linear growth…

math.AP2014★ 3 cited

Bifurcation curves of a logistic equation when the linear growth rate crosses a second eigenvalue

Pedro M. Girão

We construct the global bifurcation curves, solutions versus level of harvesting, for the steady states of a diffusive logistic equation on a bounded domain, under Dirichlet bounda…

gr-qc2014★ 53 cited

On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 3: Mass inflation and extendibility of the solutions

João L. Costa, Pedro M. Girão, José Natário +1

This paper is the third part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system w…

gr-qc2014★ 41 cited

On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 2: Structure of the solutions and stability of the Cauchy horizon

João L. Costa, Pedro M. Girão, José Natário +1

This paper is the second part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system…

gr-qc2014★ 38 cited

On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 1: Well posedness and breakdown criterion

João L. Costa, Pedro M. Girão, José Natário +1

This paper is the first part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system w…