Related papers: Restriction and decoupling estimates for the hyper…

We note that the subpolynomial factor for the $\ell^qL^p$ small cap decoupling constants for the truncated parabola $\mathbb{P}^1=\{(t,t^2):|t|\leq 1\}$ may be controlled by a suitable power of $\log R$. This is achieved by considering a…

This result sharpens the bilinear to linear deduction of Lee and Vargas for extension estimates on the hyperbolic paraboloid in $\mathbb R^3$ to the sharp line, leading to the first scale-invariant restriction estimates, beyond the…

We investigate the scalar potential of a general $S_3$-symmetric three-Higgs-doublet model. The outcome of our analysis does not depend on the fermionic sector of the model. We identify a decoupling limit for the scalar spectrum of this…

We prove a limited range, off-diagonal extrapolation theorem that generalizes a number of results in the theory of Rubio de Francia extrapolation, and use this to prove a limited range, multilinear extrapolation theorem. We give two…

In this note, we continue our research on Fourier restriction for hyperbolic surfaces, by studying local perturbations of the hyperbolic paraboloid $z=xy,$ which are of the form $z=xy+h(y),$ where $h(y)$ is a smooth function of finite type.…

A new decomposition for frequency-localized solutions to the Schrodinger equation is given which describes the evolution of the wavefunction using a weighted sum of Lipschitz tubes. As an application of this decomposition, we provide a new…

We study a class of degenerate parabolic and elliptic equations in divergence form in the upper half space $\{x_d>0\}$. The leading coefficients are of the form $x_d^2a_{ij}$, where $a_{ij}$ are bounded, uniformly elliptic, and measurable…

We consider constrained partial differential equations of hyperbolic type with a small parameter $\varepsilon>0$, which turn parabolic in the limit case, i.e., for $\varepsilon=0$. The well-posedness of the resulting systems is discussed…

We obtain some sharp $L^p$ weighted Fourier restriction estimates of the form $\|Ef\|_{L^p(B^{n+1}(0,R),Hdx)} \lessapprox R^{\beta}\|f\|_2$, where $E$ is the Fourier extension operator over the truncated paraboloid, and $H$ is a weight…

In this article, we prove that all global, nonendpoint Fourier restriction inequalities for the paraboloid in $\mathbb R^{1+d}$ have extremizers and that $L^p$-normalized extremizing sequences are precompact modulo symmetries. This result…

We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…

We prove weighted and mixed-norm Sobolev estimates for fully nonlinear elliptic and parabolic equations in the whole space under a relaxed convexity condition with almost VMO dependence on space-time variables. The corresponding interior…

We consider a loosely coupled, non-iterative Robin-Robin coupling method proposed and analyzed in [J. Numer. Math., 31(1):59--77, 2023] for a parabolic-parabolic interface problem and prove estimates for the discrete time derivatives of the…

We prove sharp bounds for the size of superlevel sets $\{x\in \mathbb{R}^2:|f(x)|>\alpha\}$ where $\alpha>0$ and $f:\mathbb{R}^2\to\mathbb{C}$ is a Schwartz function with Fourier transform supported in an $R^{-1}$-neighborhood of the…

We consider a degenerate hyperbolic equation of Kirchhoff type with a small parameter epsilon in front of the second-order time-derivative. In a recent paper, under a suitable assumption on initial data, we proved decay-error estimates for…

We prove that a family of complex hyperbolic ultra-parallel $[m_1, m_2, m_3]$-triangle group representations, where \( m_3 > 0 \), is discrete and faithful if and only if the isometry \( R_1(R_2R_1)^nR_3 \) is non-elliptic for some positive…

Suppose $0 < \alpha \leq n$, $H: \Bbb R^n \to [0,1]$ is a Lebesgue measurable function, and $A_\alpha(H)$ is the infimum of all numbers $C$ for which the inequality $\int_B H(x) dx \leq C R^\alpha$ holds for all balls $B \subset \Bbb R^n$…

Hyperbolic elliptic parabolic disks can be described by the inequality $\frac{x^2}{C^2}+2y^2-2y\leq0$ ($0<C<1$) in the unit disk based Beltrami--Cayley--Klein model of the hyperbolic geometry, up to hyperbolic congruences. The hyperbolic…

This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of…

We establish Harnack's estimates for positive weak solutions to a mixed local and nonlocal doubly nonlinear parabolic equation. All results presented in this paper are provided together with quantitative estimates.