Related papers: The $L^p$ restriction bounds for Neumann data on s…

We prove non-autonomous maximal $L^p$-regularity results on UMD spaces replacing the common H\"older assumption by a weaker fractional Sobolev regularity in time. This generalizes recent Hilbert space results by Dier and Zacher. In…

We prove an upper bound for the volume-normalized second nonzero eigenvalue of the Laplace operator on closed Riemannian manifold, in terms of the conformal volume. This bound provides effective upper bound for a large class of manifolds,…

We use the averaged variational principle introduced in a recent article on graph spectra [7] to obtain upper bounds for sums of eigenvalues of several partial differential operators of interest in geometric analysis, which are analogues of…

In this paper, we investigate the existence and uniqueness of solutions for the following model problem, involving singularities and inhomogeneous Robin boundary conditions \begin{equation*} \left\{ \begin{array}{ll}…

We establish a lower bound and an upper bound to the sum of the Fractional-Logarithmic Laplacian. A main challenge in such a study comes from the fact that this operator has a Fourier symbol that is not globally monotone in its radial…

In this manuscript we deal with regularity issues and the asymptotic behaviour (as $p \to \infty$) of solutions for elliptic free boundary problems of $p-$Laplacian type ($2 \leq p< \infty$): \begin{equation*} -\Delta_p u(x) +…

Let \phi\ be a Dirichlet or Neumann eigenfunction of the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We prove lower bounds for the size of the nodal set {\phi=0}.

\small{In 2004, Del Pino and Dolbeault \cite{DPDo} and Gentil \cite{G} investigated, independently, best constants and extremals associated to sharp Euclidean $L^p$-entropy inequalities. In this work, we present some important advances in…

In this paper we study maximal directional singular integral operators in $ \mathbb{R}^n $ given by a H\"ormander--Mihlin multiplier on an $ (n-1)$-dimensional subspace and acting trivially in the perpendicular direction. The subspace is…

We investigate the limiting behavior of solutions to the inhomogeneous $p$-Laplacian equation $-\Delta_p u = \mu_p$ subject to Neumann boundary conditions. For right hand sides which are arbitrary signed measures we show that solutions…

Let $\Omega$ be a $C^4$-smooth bounded pseudoconvex domain in $\mathbb{C}^2$. We show that if the $\overline{\partial}$-Neumann operator $N_1$ is compact on $L^2_{(0,1)}(\Omega)$ then the embedding operator…

We consider several problems related to the restriction of $(\nabla^k) \hat{f}$ to a surface $\Sigma \subset \mathbb R^d$ with nonvanishing Gauss curvature. While such restrictions clearly exist if $f$ is a Schwartz function, there are few…

We present existence and nonexistence results on the solution of an overdetermined problem for the normalized p-Laplacian in a bounded open set, with p ranging from 1 to infinity. More precisely we consider a non-constant Neumann condition…

We obtain L^p eigenfunction bounds for the harmonic oscillator in R^n and for other related operators, improving earlier results of Thangavelu and Karadzhov. We also construct suitable counterexamples which show that our estimates are…

We establish the $L^p$-$L^q$-boundedness of subelliptic pseudo-differential operators on a compact Lie group $G$. Effectively, we deal with the $L^p$-$L^q$-bounds for operators in the sub-Riemmanian setting because the subelliptic classes…

$L^p$ to $L^p_{\beta}$ boundedness theorems are proven for translation invariant averaging operators over hypersurfaces in Euclidean space. The operators can either be Radon transforms or averaging operators with multiparameter fractional…

In this paper we provide a way of taking $L^p$, $p > \frac{m}{2}$ bounds on a $m-$ dimensional Riemannian metric and transforming that into H\"{o}lder bounds for the corresponding distance function. One can think of this new estimate as a…

Let $\Omega$ be an $n$-dimensional compact Riemannian manifold $(n \geq 3)$ with $C^\infty$ boundary, and consider $L^2$-normalized eigenfunctions $ - \Delta \phi_{\lambda} = \lambda^2 \phi_\lambda$ with Dirichlet or Neumann boundary…

We apply techniques from harmonic analysis to study the $L^p$ norms of Maass forms of varying level on a quaternion division algebra. Our first result gives a candidate for the local bound for the sup norm in terms of the level, which is…

Given a domain above a Lipschitz graph, we establish solvability results for strongly elliptic second-order systems in divergence-form, allowed to have lower-order (drift) terms, with $L^p$-boundary data for $p$ near $2$ (more precisely, in…