Related papers: On the Hardy-Poincar\'e inequality with boundary s…

In this paper we study vector-valued almost minimizers of the energy functional $$ \int_D\left(|\nabla\mathbf{u}|^2+2|\mathbf{u}|\right)\,dx . $$ We establish the regularity for both minimizers and the "regular" part of the free boundary.…

We prove the existence of minimizers for some constrained variational problems on $BV(\Omega)$, under subcritical and critical restrictions, involving the affine energy introduced by Zhang in \cite{Z}. Related functionals have non-coercive…

The paper is concerned with sharp estimates of constants in Poincare type inequalities for functions having zero mean value on the boundary of a Lipschitz domain or on a measurable part of it. These estimates are useful for various…

Local minimizers of integral functionals of the calculus of variations are analyzed under growth conditions dictated by different lower and upper bounds for the integrand. Growths of non-necessarily power type are allowed. The local…

For the Alt-Caffarelli problem, we study free boundary regularity of energy minimizers. In six dimensions, we show that free boundaries are analytic for generic boundary data. In general, we improve previous generic Hausdorff dimensions of…

We study two notions of Dirichlet problem associated with BV energy minimizers (also called functions of least gradient) in bounded domains in metric measure spaces whose measure is doubling and supports a $(1,1)$-Poincar\'e inequality.…

In this short note, we provide a quantitative global Poincar\'e inequality for one forms on a closed Riemannian four manifold, in terms of an upper bound on the diameter, a positive lower bound on the volume, and a two-sided bound on Ricci…

In this work we prove some abstract results about the existence of a minimizer for locally Lipschitz functionals, without any assumption of homogeneity, over a set which has its definition inspired in the Nehari manifold. As applications we…

Let $\Omega\subset\BBR^N$ be a bounded $C^2$ domain and $\CL_\gk=-\Gd-\frac{\gk}{d^2}$ the Hardy operator where $d=\dist (.,\prt\Gw)$ and $0<\gk\leq\frac{1}{4}$. Let $\ga_{\pm}=1\pm\sqrt{1-4\gk}$ be the two Hardy exponents, $\gl_\gk$ the…

It has recently been established byWang and Xia [WX] that local minimizers of perimeter within a ball subject to a volume constraint must be spherical caps or planes through the origin. This verifies a conjecture of the authors and is in…

The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…

In this paper we prove the~existence of two non-trivial weak solutions of Dirichlet boundary value problem for p-Laplacian problem with a~singular part and two disturbances satisfying the~proper assumptions. The~abstract existence result we…

The theory of boundary regularity for $p$-harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a $p$-Poincar\'e inequality, $1<p<\infty$. The barrier classification of regular…

We study a Riemannian manifold equipped with a density which satisfies the Bakry--\'Emery Curvature-Dimension condition (combining a lower bound on its generalized Ricci curvature and an upper bound on its generalized dimension). We first…

Our goal in this paper is to find a characterization of $n$-dimensional bilinear Hardy inequalities \begin{align*} \bigg\| \,\int_{B(0,\cdot)} f \cdot \int_{B(0,\cdot)} g \,\bigg\|_{q,u,(0,\infty)} & \leq C \, \|f\|_{p_1,v_1,{\mathbb R}^n}…

We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some…

We prove new boundary Harnack inequalities in Lipschitz domains for equations with a right hand side. Our main result applies to non-divergence form operators with bounded measurable coefficients and to divergence form operators with…

In \cite{CHMY04}, we studied $p$-mean curvature and the associated $p$-minimal surfaces in the Heisenberg group from the viewpoint of PDE and differential geometry. In this paper, we look into the problem through the variational…

We shall investigate the boundedness of the intrinsic square functions and their commutators on generalized weighted Orlicz-Morrey spaces $M^{\Phi,\varphi}_{w}({\mathbb R}^n)$. In all the cases, the conditions for the boundedness are given…

We consider the existence and the non-existence of a minimizer of the following minimization problems associated with an improved Hardy-Sobolev type inequality introduced by Ioku. $$ I_a := \inf_{u \in W_0^{1,p}(B_R ) \setminus \{ 0\} }…