Related papers: Lower semicontinuity for an integral functional in…

In this paper we provide a different approach for existence of the variational solutions of the gradient flows associated to functionals on Sobolev spaces studied in \cite{BDDMS20}. The crucial condition is the convexity of the functional…

An integral representation result for strictly positive subharmonic functions of a one-dimensional regular diffusion is established. More precisely, any such function can be written as a linear combination of an increasing and a decreasing…

We study the existence and the properties of the reduced measures for the parabolic equations $\partial_tu-\Delta u+g(u)=0$ in $\Omega\times (0,\infty)$ subject to the conditions ($P$): $u=0$ on $\partial\Omega\times (0,\infty)$,…

Let $\mathbb C$ be the complex plane, $E$ be a measurable subset in a segment $[0, R]$ of the positive semiaxis $\mathbb R^+$, $u\not\equiv -\infty$ be a subharmonic function on $\mathbb C$. The main result of this article is an upper…

We show the H\"older continuity of quasiminimizers of the energy functionals $\int f(x,u,\nabla u)\,dx$ with nonstandard growth under the general structure conditions $$ |z|^{p(x)} - b(x)|y|^{r(x)}-g(x) \leq f(x,y,z) \leq \mu|z|^{p(x)} +…

We give a partial uniqueness result concerning comparable renormalized solutions of the nonlinear elliptic problem $-\diw(\aop(x,Du))=\mu$ in $\Omega$, $u=0$ on $\partial\Omega$, where $\mu$ is a Radon measure with bounded variation on…

Let $M$ be a complete non-compact Riemannian manifold and let $\sigma $ be a Radon measure on $M$. We study the problem of existence or non-existence of positive solutions to a semilinear elliptic inequaliy \begin{equation*} -\Delta u\geq…

We extend the classical Kato's inequality in order to allow functions $u \in L^1_\mathrm{loc}$ such that $\Delta u$ is a Radon measure. This inequality has been applied by Brezis, Marcus, and Ponce to study the existence of solutions of the…

Given a Radon measure $\mu$ on $R^d$, which may be non doubling, we introduce a space of type BMO with respect to this measure. It is shown that many properties that hold when $\mu$ is doubling remain valid for the space BMO introduced in…

We study the semilinear elliptic equation --$\Delta$u + g(u)$\sigma$ = $\mu$ with Dirichlet boundary condition in a smooth bounded domain where $\sigma$ is a nonnegative Radon measure, $\mu$ a Radon measure and g is an absorbing…

An existence of a nontrivial solution in some `weaker' sense of the following system of equations \begin{align*} (-\Delta)^{s}u+l(x)\phi u+w(x)|u|^{k-1}u&=\mu~\text{in}~\Omega\nonumber\\ (-\Delta)^{s}\phi&=…

We study the BMO-type functional $\kappa_{\varepsilon}(f,\mathbb R^n)$, which can be used to characterize BV functions $f\in BV(\mathbb R^n)$. The $\Gamma$-limit of this functional, taken with respect to $L^1_{\mathrm{loc}}$-convergence, is…

We deal with existence, uniqueness, and regularity for solutions of the boundary value problem $$ \begin{cases} {\mathcal L}^s u = \mu &\quad \text{in $\Omega$}, u(x)=0 \quad &\text{on} \ \ \mathbb{R}^N\backslash\Omega, \end{cases} $$ where…

We compute the fully-differential B -> X_u l nu decay width to all orders in perturbation theory in the large-beta0 limit. Each of the five structure functions that build the hadronic tensor is expressed as a Borel integral, summing up O(CF…

The following is an overview of the measurements of the CKM matrix elements V_cb and V_ub that are based on detailed studies of semileptonic B decays by the BABAR and Belle Collaborations and recent advances in QCD calculations. In…

In this paper we prove a lower semicontinuity result of Reshetnyak type for a class of functionals which appear in models for small-strain elasto-plasticity coupled with damage. To do so we characterise the limit of measures…

In this paper we prove a H\"older partial regularity result for weak solutions $u:\Omega\to \mathbb{R}^N$, $N\geq 2$, to non-autonomous elliptic systems with general growth of the type: \begin{equation*} -\rm{div}\, a(x, u, Du)= b(x, u, Du)…

We consider semilinear equation of the form $-Lu=f(x,u)+\mu$, where $L$ is the operator corresponding to a transient symmetric regular Dirichlet form ${\mathcal E}$, $\mu$ is a diffuse measure with respect to the capacity associated with…

We prove an $\varepsilon$-regularity theorem for $BV^\mathcal{B}$ minimizers of strongly $\mathcal{B}$-quasiconvex functionals with linear growth, where $\mathcal{B}$ is an elliptic operator of the first order. This generalises to the…

Let $U\not\equiv \pm\infty$ be a $\delta$-subharmonic function on a closed disc of radius $R$ centered at zero. In the previous two parts of our paper, we obtained general and explicit estimates of the integral of the positive part of the…