A SHARP SOBOLEV INEQUALITY ON RIEMANNIAN MANIFOLDS ∗ (2008)
Abstract. Let (M, g) be a smooth compact Riemannian manifold without boundary of dimension n ≥ 6. We prove that
Some sharp Hardy inequalities on spherically symmetric domains (2008)
Chiacchio, Francesco, Ricciardi, Tonia
We prove some sharp Hardy inequalities for domains with a spherical symmetry. In particular, we prove an inequality for domains of the unit $n$-dimensional sphere with a point singularity, and an...
A sharp Wirtinger inequality and some related functional spaces (2008)
Giova, Raffaella, Ricciardi, Tonia
We consider the generalized Wirtinger inequality \[ (\int_{0}^{T} a |u|^q )^{1/q} \le C \biggm(\int_{0}^{T} a^{1-p} |u'|^{p}\biggm)^{1/p}, \] with $p,q>1$, $T>0$, $a\in L^1[0,T]$, $a\ge0$,...
On planar Beltrami equations and Hoelder regularity (2006)
We provide estimates for the H\"older exponent of solutions to the Beltrami equation $\dbar f=\mu\de f+\nu\bar{\de f}$, where the Beltrami coefficients $\mu,\nu$ satisfy $\||\mu|+|\nu|\|_\infty
Mountain pass solutions for a mean field equation from two-dimensional turbulence (2006)
Using Struwe's "monotonicity trick" and the recent blow-up analysis of Ohtsuka and Suzuki, we prove the existence of mountain pass solutions to a mean field equation arising in two-dimensional...
On Beltrami equations and Hoelder regularity (2006)
We estimate the Hoelder exponent $\alpha$ of solutions to the Beltrami equation $\dbar f=\mu\de f$, where the Beltrami coefficient satisfies $\|\mu\|_\infty
On the best Hoelder exponent for two dimensional elliptic equations in divergence form (2005)
We obtain an estimate for the H\"older continuity exponent for weak solutions to the following elliptic equation in divergence form: \[ \mathrm{div}(A(x)\nabla u)=0 \qquad\mathrm{in\}\Omega, \] where...
A sharp weighted Wirtinger inequality (2005)
We obtain a sharp estimate for the best constant $C>0$ in the Wirtinger type inequality \[ \int_0^{2\pi}\gamma^pw^2\le C\int_0^{2\pi}\gamma^qw'^2 \] where $\gamma$ is bounded above and below away...
A shadowing lemma for abelian Higgs vortices (2004)
Macri', Marta, Nolasco, Margherita, Ricciardi, Tonia
We use a shadowing-type lemma in order to analyze the singular, semilinear elliptic equation describing static self-dual abelian Higgs vortices. Such an approach allows us to construct new solutions...
A sharp H\"older estimate for elliptic equations in two variables (2004)
We prove a sharp H\"older estimate for solutions of linear two-dimensional, divergence form elliptic equations with measurable coefficients, such that the matrix of the coefficients is symmetric and...
Multiple vortices for a self-dual CP(1) Maxwell-Chern-Simons model (2003)
Chiacchio, Francesco, Ricciardi, Tonia
We prove the existence of at least two doubly periodic vortex solutions for a self-dual CP(1) Maxwell-Chern-Simons model. To this end we analyze a system of two elliptic equations with exponential...
We prove the existence of at least two solutions for a fourth order equation, which includes the vortex equations for the U(1) and CP(1) self-dual Maxwell-Chern-Simons models as special cases. Our...
On a nonlinear elliptic system from Maxwell-Chern-Simons vortex theory (2002)
We define an abstract nonlinear elliptic system, admitting a variational structure, and including the vortex equations for some Maxwell-Chern-Simons gauge theories as special cases. We analyze the...
A sharp Sobolev inequality on Riemannian manifolds (2002)
Let (M,g) be a smooth compact Riemannian manifold without boundary of dimension n>=6. We prove that {align*} \|u\|_{L^{2^*}(M,g)}^2 \le K^2\int_M\{|\nabla_g u|^2+c(n)R_gu^2\}dv_g...