Related papers: A Priori Estimates for Maximally Subelliptic Quadr…
We give an upper bound for the number of rational points of height at most $B$, lying on a surface defined by a quadratic form $Q$. The bound shows an explicit dependence on $Q$. It is optimal with respect to $B$, and is also optimal for…
The goal of this paper is to establish sharp two-sided estimates on the heat kernels of two types of purely discontinuous symmetric Markov processes in the upper half-space of $\mathbb R^d$ with jump kernels degenerate at the boundary. The…
The notion of quasi boundary triples and their Weyl functions is an abstract concept to treat spectral and boundary value problems for elliptic partial differential equations. In the present paper the abstract notion is further developed,…
We provide an asymptotic estimate for the number of rational points of bounded height on a non-singular conic over the rationals. The estimate is uniform in the coefficients of the underlying quadratic form.
In this paper, we derive a priori estimates for the gradient and second order derivatives of solutions to a class of Hessian type fully nonlinear parabolic equations with the first initial-boundary value problem on Riemannian manifolds.…
In the present paper, we solve three boundary value problems related to the temperature field in oil strata -- the fractional extensions of the incomplete lumped formulation and lumped formulation in the linear case and the fractional…
We give an abstract argument that an a priori Fourier restriction estimate for a certain choice of exponents automatically implies maximal and variational Fourier restriction estimates. These, in turn, provide pointwise and quantitative…
We study weighted simultaneous rational approximation to points of the form $(1,\xi,\xi^2)$, for a class of extremal real numbers $\xi$, within the framework of multi-parametric geometry of numbers.
In a domain of the Euclidean space, we estimate from below the distance to the boundary of global maximum points of solutions of elliptic and parabolic equations with homogeneous Dirichlet boundary values. As reference cases, we first…
This paper extends previous work on linear correlations of representation functions of positive definite binary quadratic forms to allow indefinite forms.
We obtain fundamental imbeddings for the fractional Sobolev space with variable exponent that is a generalization of well-known fractional Sobolev spaces. As an application, we obtain a-priori bounds and multiplicity of solutions to some…
The paper deals with point-wise estimates for the heat kernel of a nonlocal convolution type operator with a kernel that decays at least exponentially at infinity. It is shown that the large time behaviour of the heat kernel depends…
In this work, new theoretical results on functional type a posteriori estimates for elliptic optimal control problems with control constraints are presented. More precisely, we derive new, sharp, guaranteed and fully computable lower bounds…
We derive a priori estimates for the incompressible free-boundary Euler equations with surface tension in three spatial dimensions. Working in Lagrangian coordinates, we provide a priori estimates for the local existence when the initial…
We provide sharp boundary regularity estimates for solutions to elliptic equations driven by an integro-differential operator obtained as the sum of a Laplacian with a nonlocal operator generalizing a fractional Laplacian. Our approach…
We give some results on a priori estimates and on estimates of type sup+inf and sup*inf.
In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with nonmonotone multivalued subdifferential boundary condition on a portion of the boundary…
Weighted quadratic estimates are proved for certain bisectorial firstorder differential operators with bounded measurable coefficients which are (not necessarily pointwise) accretive, on complete manifolds with positive injectivity radius.…
This work introduces novel numerical algorithms for computational quantum mechanics, grounded in a representation of the Laplace operator -- frequently used to model kinetic energy in quantum systems -- via the heat semigroup. The key…
We derive localized and global noncompact versions of Hamilton's gradient estimate for positive solutions to the heat equation on Riemannian manifolds with Ricci curvature bounded below. Our estimates are essentially optimal and…