相关论文: Test function approach to fully nonlinear equation…
We consider the Cahn-Hilliard equation with Neumann boundary conditions in a three-dimensional curved thin domain around a given closed surface. When the thickness of the curved thin domain tends to zero, we show that the weighted average…
We study the fractional Laplacian $(-\Delta)^{\sigma/2}$ on the $n$-dimensional torus $\mathbb{T}^n$, $n\geq1$. First, we present a general extension problem that describes \textit{any} fractional power $L^\gamma$, $\gamma>0$, where $L$ is…
In this note we study the application of generalized fractional operators to a particular class of nonstandard Lagrangians. These are typical of dissipative systems and the corresponding Euler-Lagrange and Hamilton equations are analyzed.…
Using tools from quantum harmonic analysis, we show that the domain of the Laplacian of an operator is dense in the Toeplitz algebra over the Fock space $\mathcal{F}^2(\mathbb{C}^n)$. As an application, we provide a simplified treatment of…
We prove that the $\bar\partial$-Neumann solution operator is locally regular in a domain which has compactness estimates, is of finite type outside a curve transversal to the CR directions and for which the holomorphic tangential…
We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem in perforated domains.
In this paper, we investigate a rather general system of two operator equations that has the structure of a viscous or nonviscous Cahn--Hilliard system in which nonlinearities of double-well type occur. Standard cases like regular or…
We calculate the regional fractional Laplacian on some power function on an interval. As an application, we prove Hardy inequality with an extra term for the fractional Laplacian on the interval with the optimal constant. As a result, we…
We give a simple and more elementary proof that the notions of Domain of Holomorphy and Weak Domain of Holomorphy are equivalent. This proof is based on a combination of Baire's Category Theorem and Montel's Theorem. We also obtain…
The fractional Laplacian can be obtained as a Dirichlet-to-Neumann map via an extension problem to the upper half space. In this paper we prove the same type of characterization for the fractional powers of second order partial differential…
In this work, some non smooth bilinear analogues of linear Littlewood-Paley square functions on the real line are studied. These bilinear operators are closely related to the bilinear Hilbert transforms and vector valued version of these…
In this note we describe how the Neumann homogenization of fully nonlinear elliptic equations can be recast as the study of nonlocal (integro-differential) equations involving elliptic integro-differential operators on the boundary. This is…
We introduce a general coupled system of parabolic equations with quadratic nonlinear terms and diffusion terms defined by fractional powers of the Laplacian operator. We develop a method to establish the rigorous convergence of the…
In this dissertation we explore the $[L^{\mathrm{p}},\ L^{q}]$-boundedness of certain integral operators on weighted spaces on cones in ${\mathbb R}^{n}.$ These integral operators are of the type $\displaystyle \int_{V}k(x,\ y)f(y)dy$…
We provide estimates for the convolution product of an arbitrary number of "resurgent functions", that is holomorphic germs at the origin of $C$ that admit analytic continuation outside a closed discrete subset of $C$ which is stable under…
We prove sharp inequalities for determinants of Toeplitz operators and twisted Laplace operators on the two-sphere, generalizing the Moser-Trudinger-Onofri inequality. In particular a sharp version of conjectures of Gillet-Soule and Fang…
We prove the Harnack inequality for antisymmetric $s$-harmonic functions, and more generally for solutions of fractional equations with zero-th order terms, in a general domain. This may be used in conjunction with the method of moving…
We prove convergence of a sequence of weak solutions of the nonlocal Cahn-Hilliard equation to the strong solution of the corresponding local Cahn-Hilliard equation. The analysis is done in the case of sufficiently smooth bounded domains…
In a recent paper we have presented a method to evaluate certain Hankel determinants as almost products; i.e. as a sum of a small number of products. The technique to find the explicit form of the almost product relies on…
We present some results on a fully nonlinear version of the Yamabe problem and a Harnack type inequality for general conformally invariant fully nonlinear second order elliptic equations.