arXiv subjects
Publications and source records attributed to Sunra Mosconi.
A short account of recent existence and multiplicity theorems on the Dirichlet problem for an elliptic equation with $(p,q)$-Laplacian in a bounded domain is performed. Both eigenvalue problems and different types of perturbation terms are briefly discussed. Special attention is paid to possibly coercive, resonant, subcritical, critical, or asymmetric right-hand sides.
By virtue of a suitable approximation argument, we prove a Pohozaev identity for nonlinear nonlocal problems on $\mathbb{R}^N$ involving the fractional $p-$Laplacian operator. Furthermore we provide an application of the identity to show that some relevant levels of the energy functional associated with the problem coincide.
We overview some recent existence and regularity results in the theory of nonlocal nonlinear problems driven by the fractional $p$-Laplacian.
In this paper, we discuss several results regarding existence, non-existence and asymptotic properties of solutions to $u""+qu"+f(u)=0$, under various hypotheses on the parameter $q$ and on the potential $F(t)=\int_0^tf(s)\, ds$, generally assumed to be bounded from below. We prove a non-existence result in the case $q\le 0$ and an existence result of periodic solution for: 1) almost every suitably small (depending on $F$), positive values of $q$; 2) all suitably large (depending on $F$) values of $q$. Finally, we describe some conditions on $F$ which ensure that some (or all) solutions $u_q$ to the equation satisfy $\|u_q\|_\infty\to 0$, as $q\downarrow 0$.
We obtain the sharp asymptotic behavior at infinity of extremal functions for the fractional critical Sobolev embedding.
We study the asymptotic behavior of solutions to the nonlocal nonlinear equation $(-Δ_p)^s u=|u|^{q-2}u$ in a bounded domain $Ω\subset{\mathbb R}^N$ as $q$ approaches the critical Sobolev exponent $p^*=Np/(N-ps)$. We prove that ground state solutions concentrate at a single point $\bar x\in \overlineΩ$ and analyze the asymptotic behavior for sequences of solutions at higher energy levels. In the semi-linear case $p=2,$ we prove that for smooth domains the concentration point $\bar x$ cannot lie on the boundary, and identify its location in the case of annular domains.
By virtue of barrier arguments we prove $C^α$-regularity up to the boundary for the weak solutions of a non-local nonlinear problem driven by the fractional $p$-Laplacian operator. The equation is boundedly inhomogeneous and the boundary conditions are of Dirichlet type. We employ different methods according to the singular ($p<2$) of degenerate ($p>2$) case.
We obtain nontrivial solutions to the Brezis-Nirenberg problem for the fractional $p$-Laplacian operator, extending some results in the literature for the fractional Laplacian. The quasilinear case presents two serious new difficulties. First an explicit formula for a minimizer in the fractional Sobolev inequality is not available when $p \ne 2$. We get around this difficulty by working with certain asymptotic estimates for minimizers recently obtained by Brasco, Mosconi and Squassina. The second difficulty is the lack of a direct sum decomposition suitable for applying the classical linking theorem. We use an abstract linking theorem based on the cohomological index proved by Perera and Yang to overcome this difficulty.
We consider a boundary value problem driven by the fractional p-Laplacian operator with a bounded reaction term. By means of barrier arguments, we prove Hölder regularity up to the boundary for the weak solutions, both in the singular (1 2) case.
We prove the existence of a positive solution for nonlocal problems involving the fractional Laplacian and a critical growth power nonlinearity when the equation is set in a suitable contractible domain.
We study a class of semi-linear problems involving the fractional Laplacian under subcritical or critical growth assumptions. We prove that, for the corresponding functional, local minimizers with respect to a C^0-topology weighted with a suitable power of the distance from the boundary are actually local minimizers in the natural H^s-topology.
We prove an abstract and general version of the Lewy-Stampacchia inequality. We then show how to reproduce more classical versions of it and, more importantly, how it can be used in conjunction with Laplacian comparison estimates to produce large class of functions with bounded Laplacian on spaces with a lower bound on the Ricci curvature.
We prove that the Abresch-Gromoll inequality holds on infinitesimally Hilbertian CD(K,N) spaces in the same form as the one available on smooth Riemannian manifolds.