相关论文: A note on the moving hyperplane method
Persistence diagrams, combining geometry and topology for an effective shape description used in pattern recognition, have already proven to be an effective tool for shape representation with respect to a certainfiltering function.…
H\"older estimates for second derivatives are proved for solutions of fully nonlinear parabolic equations in two space variables. Related techniques extend the regularity theory for fully nonlinear parabolic equations in higher dimensions.
We prove regularity estimates for time derivatives of a large class of nonlinear parabolic partial differential systems. This includes the instationary (symmetric) p-Laplace system and models for non Newtonien fluids of powerlaw or Carreau…
We derive a global higher regularity result for weak solutions of the linear relaxed micromorphic model on smooth domains. The governing equations consist of a linear elliptic system of partial differential equations that is coupled with a…
The article is devoted to the study of mappings that satisfy the so-called inverse Poletsky inequality. We consider mappings of quasiextremal distance domains, domains with a locally quasiconformal boundary, and domains which are regular in…
Hardy property of means has been extensively studied by P\'ales and Pasteczka since 2016. The core of this research is based on few of their properties: concavity, symmetry, monotonicity, repetition invariance and homogeneity (last axiom…
In recent years, several numerical methods for solving the unique continuation problem for the wave equation in a homogeneous medium with given data on the lateral boundary of the space-time cylinder have been proposed. This problem enjoys…
We show that, for disjoint domains in the Euclidean space, mutual absolute continuity of their harmonic measures implies absolute continuity with respect to surface measure and rectifiability in the intersection of their boundaries. This…
Let $f$ be a meromorphic correspondence on a compact K\"ahler manifold $X$ of dimension $k$. Assume that its topological degree is larger than the dynamical degree of order $k-1$. We obtain a quantitative regularity of the equilibrium…
In this paper we prove the continuity of stable subspaces associated to parabolic-hyperbolic boundary value problems, for limiting values of parameters. The analysis is based on the construction performed in a previous paper of Kreiss' type…
It is shown that if the sequence $(p_j(x))$ increases uniformly to $p(x)$ in a bounded, smooth domain $\Omega$, then the sequence $(u_i)$ of solutions to the Dirichlet problem for the $p_i(x)$-Laplacian with fixed boundary datum $\varphi$…
The relationship between overparameterization, stability, and generalization remains incompletely understood in the setting of discontinuous classifiers. We address this gap by establishing a generalization bound for finite function classes…
This article introduces the Modified Parameterized Leapfrog Hamiltonian Monte Carlo (MPL-HMC) method, a novel extension of HMC addressing key limitations through tunable integration parameters $\alpha(\delta t)$ and $\beta(\delta t)$,…
Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…
In this paper, we derive from the principle of least action the equation of motion for a continuous medium with regularized density field in the context of measures. The eventual equation of motion depends on the order in which…
The aim of this paper is to develop the regularity theory for a weak solution to a class of quasilinear nonhomogeneous elliptic equations, whose prototype is the following mixed Dirichlet $p$-Laplace equation of type \begin{align*}…
In this note we show how to adjust some proofs of Koskela et. al 2003 and Jiang 2011 in order to show that in certain spaces $(X,d,\mu)$, like $RCD(K,N)$-spaces, every Sobolev function with local $L^{p}$-Laplacian and $p>\dim\mu$ is locally…
Consider a Lipschitz domain $\Omega$ and a measurable function $\mu$ supported in $\overline\Omega$ with $\left\|{\mu}\right\|_{L^\infty}<1$. Then the derivatives of a quasiconformal solution of the Beltrami equation $\overline{\partial} f…
This paper is concerned with quasilinear parabolic reaction-diffusion-advection systems on extended domains. Frameworks for well-posedness in Hilbert spaces and spaces of continuous functions are presented, based on known results using…