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We investigate the Westervelt equation with several versions of nonlinear damping and lower order damping terms and Neumann as well as absorbing boundary conditions. We prove local in time existence of weak solutions under the assumption…
This is an expository paper on the theory of local regularity for weak solutions to the non-stationary 3D Navier-Stokes equations near the boundary of a domain.
The standard mixed finite element approximations of Hodge Laplace problems associated with the de Rham complex are based on proper discrete subcomplexes. As a consequence, the exterior derivatives, which are local operators, are computed…
Laplace approximation is a very useful tool in Bayesian inference and it claims a nearly Gaussian behavior of the posterior. \cite{SpLaplace2022} established some rather accurate finite sample results about the quality of Laplace…
Recent works have derived non-asymptotic upper bounds for convergence of underdamped Langevin MCMC. We revisit these bound and consider introducing scaling terms in the underlying underdamped Langevin equation. In particular, we provide…
We provide novel theoretical results regarding local optima of regularized $M$-estimators, allowing for nonconvexity in both loss and penalty functions. Under restricted strong convexity on the loss and suitable regularity conditions on the…
Aim of the paper is to study non-local dynamic boundary conditions of reactive-diffusive type for the Laplace equation from analytic and probabilistic point of view. In particular, we provide compact and probabilistic representation of the…
For the zone of moderate deviation probabilities the local asymptotic minimax lower bound of asymptotic efficiency of estimators is established. The estimation parameter is multidimensional. The lower bound admits the interpretation as the…
A new idea to approximate the second eigenfunction and the second eigenvalue of $p$-Laplace operator is given. In the case of the Dirichlet boundary condition, the scheme has the restriction that the positive and the negative part of the…
The Laplace approximation is sometimes not sufficiently accurate for smoothing parameter estimation in generalized additive mixed models. A novel estimation strategy is proposed that solves this problem and leads to estimates exhibiting the…
Given a bounded domain, we deal with the problem of estimating the distance function from the internal points of the domain to the boundary of the domain. Convolutional and differential distance estimation schemes are considered and, for…
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…
We discuss the divergence problems recently identified in some extrapolation operators for weakly-relational numeric domains. We identify the cause of the divergences and point out that resorting to more concrete, syntactic domains can be…
The paper introduces a general strategy for identifying strong local minimizers of variational functionals. It is based on the idea that any variation of the integral functional can be evaluated directly in terms of the appropriate…
In this article, by applying the well known method for dealing with $p$-Laplace type elliptic boundary value problems, the authors establish a sharp estimate for the decreasing rearrangement of the gradient of solutions to the Dirichlet and…
We establish a general sufficient condition for a sequence of Galton Watson branching processes in varying environment to converge weakly. This condition extends previous results by allowing offspring distributions to have infinite…
We give explicit and asymptotic lower bounds for the quantity $|e^{s/t}-M/N|$ by studying a generalized continued fraction expansion of $e^{s/t}$. In cases $|s|\geq 3$ we improve existing results by extracting a large common factor from the…
This paper presents a new formulation of the fractional Laplacian operator $(-\Delta)^s$ in $n$-dimensional space ($n \ge 1$). The proposed formulation expresses $(-\Delta)^s$ as a composition of the classical Laplace differential operator…
This paper is concerned with the derivation of computable and guaranteed upper and lower bounds of the difference between the exact and the approximate solution of a boundary value problem for static Maxwell equations. Our analysis is based…
In this short note we derive, for bounded domains, an upper bound for a Friedrichs type constant in a weighted Friedrichs type inequality. This upper bound generalizes a well known upper bound of the Friedrichs constant. This upper bound is…