Related papers: Keller--Osserman conditions for diffusion-type ope…

The evolution operator method is used to solve the generalized Fokker-Planck equations and the generalized diffusion-wave equations in the (1+1) dimensional space in which $x\in\mathbb{R}$ and $t\in\mathbb{R}_+$. These equations contain…

We investigate the nonexistence and existence of nontrivial positive solutions to $\Delta_m u+u^p|\nabla u|^q\leq0$ on noncompact geodesically complete Riemannian manifolds, where $m>1$, and $(p,q)\in \mathbb{R}^2$. According to…

We consider a Keller-Segel model with non-linear porous medium type diffusion and non-local attractive power law interaction, focusing on potentials that are less singular than Newtonian interaction. Here, the nonlinear diffusion is chosen…

We consider operators $L$ acting on functions on a Riemannian surface, $\Sigma$, of the form $L = \Delta + V +a K.$ Here $\Delta$ is the Laplacian of $\Sigma$, $V$ a non-negative potential on $\Sigma$, K the Gaussian curvature and $a$ is a…

In this paper we present examples of nondivergence form second order elliptic operators with continuous coefficients such that $L$ has an irregular boundary point that is regular for the Laplacian. Also for any eigenvalue spread <1 of the…

In this paper we are concerned with the following Kirchhoff type problem involving the 1-Laplace operator : \begin{equation*} \left\{\begin{array}{llc} u_{t}-m\left(\int_{\Omega}|Du|\right)\Delta_{1} u=0 & \text{in}\ & \Omega\times…

We consider fully nonlinear degenerate elliptic equations with zero and first order terms. We provide a priori upper bounds and characterize the existence of entire subsolutions under growth conditions on the lower order coefficients which…

In this manuscript, we study the nonlinear eigenvalue problem on complete Riemannian manifolds with Ricci curvature bounded from below, to find the unknowns $\lambda$ and $u$, such that $$ Qu + \lambda f(u) = 0 $$ where $\lambda$ is an…

We obtain a basic inequality involving the Laplacian of the warping function and the squared mean curvature of any warped product isometrically immersed in a Riemannian manifold without assuming any restriction on the Riemann curvature…

We propose an operator preconditioner for general elliptic pseudodifferential equations in a domain $\Omega$, where $\Omega$ is either in $\mathbb{R}^n$ or in a Riemannian manifold. For linear systems of equations arising from low-order…

Let $\Omega$ be a connected open subset of $\Ri^d$. We analyze $L_1$-uniqueness of real second-order partial differential operators $H=-\sum^d_{k,l=1}\partial_k\,c_{kl}\,\partial_l$ and $K=H+\sum^d_{k=1}c_k\,\partial_k+c_0$ on $\Omega$…

We investigate the one-dimensional Keller-Segel model where the diffusion is replaced by a non-local operator, namely the fractional diffusion with exponent $0<\alpha\leq 2$. We prove some features related to the classical two-dimensional…

In this paper we obtain lower bound estimates of the spectrum of Laplace-Beltrami operator on complete submanifolds with bounded mean curvature, whose ambient space admits a Riemannian submersion over a Riemannian manifold with negative…

We prove the existence of Sobolev extension operators for certain uniform classes of domains in a Riemannian manifold with an explicit uniform bound on the norm depending only on the geometry near their boundaries. We use this quantitative…

In this paper, we study Jacobi operators associated to algebraic curvature maps (tensors) on lightlike submanifolds M. We investigate conditions for an induced Rie- mann curvature tensor to be an algebraic curvature tensor on M. We…

We derive nonlinear stability results for numerical integrators on Riemannian manifolds, by imposing conditions on the ODE vector field and the step size that makes the numerical solution non-expansive whenever the exact solution is…

We discuss the existence theory of a nonlinear problem of nonlocal type subject to Neumann boundary conditions. Differently from the existing literature, the elliptic operator under consideration is obtained as a superposition of operators…

We consider the possibility of adding a Grassmann-odd function \nu to the odd Laplacian. Requiring the total \Delta operator to be nilpotent leads to a differential condition for \nu, which is integrable. It turns out that the odd function…

Let $\mathcal{M}$ be a compact, smooth, $n$-dimensional Riemannian manifold without boundary. In this paper, we generalize nonwindowed geometric scattering transforms, which we formulate as $\mathbf{L}^q(\mathcal{M})$ norms of a cascade of…

Let $M$ be an $n$-dimensional Lagrangian submanifold of a complex space form. We prove a pointwise inequality $$\delta(n_1,\ldots,n_k) \leq a(n,k,n_1,\ldots,n_k) \|H\|^2 + b(n,k,n_1,\ldots,n_k)c,$$ with on the left hand side any…