Related papers: On implicitly oscillatory quadrilinear integrals

Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…

We establish the existence of positive solutions to a general class of overdetermined semilinear elliptic boundary problems on suitable bounded open sets $\Omega\subset\mathbb{R}^n$. Specifically, for $n\leq 4$ and under mild technical…

We establish boundedness results for bilinear singular integral operators with rough homogeneous kernels whose restriction to the unit sphere belongs to the Orlicz space $L(\log L)^\alpha$. This improves the previously best known condition…

In this paper, we give a rigorous proof of the renormalizability of the massive $\phi_4^4$ theory on a half-space, using the renormalization group flow equations. We find that five counter-terms are needed to make the theory finite, namely…

For a class of systems of semi-linear elliptic equations, including \[ -\Delta u_i=f_i(x,u_i) - \beta u_i\sum_{j\neq i}a_{ij}u_j^p,\qquad i=1,\dots,k, \] for $p=2$ (variational-type interaction) or $p = 1$ (symmetric-type interaction), we…

We show that if $f$ is a nonzero, noninvertible function on a smooth complex variety $X$ and $J_f$ is the Jacobian ideal of $f$, then ${\rm lct}(f,J_f^2)>1$ if and only if the hypersurface defined by $f$ has rational singularities.…

We study the existence of global implicit functions for equations defined on open subsets of Banach spaces. The partial derivative with respect to the second variable is only required to have a left inverse instead of being invertible.…

For any 3-monotone on $[a,b]$ function $f$ (its third divided differences are nonnegative for all choices of four distinct points, or equivalently, $f$ has a convex derivative on $(a,b)$) we construct a cubic 3-monotone (like $f$) spline…

Function values are, in some sense, "almost as good" as general linear information for $L_2$-approximation (optimal recovery, data assimilation) of functions from a reproducing kernel Hilbert space. This was recently proved by new upper…

We discuss the rigorous justification of the spatial discretization by means of Fourier spectral methods of quasilinear first-order hyperbolic systems. We provide uniform stability estimates that grant spectral convergence of the…

In this note, our aim is to show that families of smooth hypersurfaces of $\mathbb R^{n+1}$ which are all $C^1$--close enough to a fixed compact, embedded one, have uniformly bounded constants in some relevant inequalities for mathematical…

A function $f:N\rightarrow N$ is sublinear, if \[\lim_{x\rightarrow +\infty}\frac{f(x)}{x}=0.\] If $A$ is an Abelian group, $G$ is a graph and $\phi$ is an $A$-flow in $G$, then let $N(\phi)$ be the nullity of $\phi$, that is, the set of…

We suggest the necessary/sufficient criteria for the existence of a (order-by-order) solution y(x) of a functional equation F(x,y)=0 over a ring. In full generality, the criteria hold in the category of filtered groups, this includes the…

We prove the stability under integration and under Fourier transform of a concrete class of functions containing all globally subanalytic functions and their complex exponentials. This paper extends the investigation started in [J.-M. Lion,…

We examine the relation between oscillatory integral estimates and sublevel set estimates associated to convex functions. Whilst the former implies the latter in many cases, the reverse requires additional assumptions. Under finite (line)…

Let $f,g_1,\dots,g_m$ be polynomials with real coefficients in a vector of variables $x=(x_1,\dots,x_n)$. Denote by $\text{diag}(g)$ the diagonal matrix with coefficients $g=(g_1,\dots,g_m)$ and denote by $\nabla g$ the Jacobian of $g$. Let…

In the context of global optimization of mixed-integer nonlinear optimization formulations, we consider smoothing univariate functions $f$ that satisfy $f(0)=0$, $f$ is increasing and concave on $[0,+\infty)$, $f$ is twice differentiable on…

We consider the nonholonomic systems of $n$ homogeneous balls $\mathbf B_1,\dots,\mathbf B_n$ with the same radius $r$ that are rolling without slipping about a fixed sphere $\mathbf S_0$ with center $O$ and radius $R$. In addition, it is…

We prove necessary and sufficient conditions for the asymptotic normality of multiple integrals with respect to a Poisson measure on a general measure space, expressed both in terms of norms of contraction kernels and of variances of…

We consider bivariate polynomials over the skew field of quaternions, where the indeterminates commute with all coefficients and with each other. We analyze existence of univariate factorizations, that is, factorizations with univariate…