Related papers: Some remarks on the comparison principle in Kirchh…
The Perron method for solving the Dirichlet problem for $p$-harmonic functions is extended to unbounded open sets in the setting of a complete metric space with a doubling measure supporting a $p$-Poincar\'e inequality, $1<p<\infty$. The…
Sinc-collocation methods are known to be efficient for Fredholm integral equations of the second kind, even if functions in the equations have endpoint singularity. However, existing methods have the disadvantage of inconsistent collocation…
We consider the Kirchhoff equation $$ \partial_{tt} u - \Delta u \Big( 1 + \int_{\mathbb T^d} |\nabla u|^2 \Big) = 0 $$ on the $d$-dimensional torus $\mathbb T^d$, and its Cauchy problem with initial data $u(0,x)$, $\partial_t u(0,x)$ of…
We show that Nederlof's algorithm [Information Processing Letters, 118 (2017), 15-16] for constructing a proof that the number of subsets summing to a particular integer equals a claimed quantity is flawed because: 1) its consistence is not…
We obtain novel criteria for the existence of local bifurcation for periodic solutions of Hamiltonian systems by a comparison principle of the spectral flow. Our method allows to find the appearance of new solutions by a simple inspection…
In this paper, we extend the investigations regarding Birkhoff-James orthogonality of linear operators to bounded continuous functions on metric spaces. We introduce Birkhoff-James extensions of continuous functions and study them in…
A new method is proposed to improve the numeri- cal simulation of time dependent problems when the initial and boundary data are not compatible. Unlike earlier methods limited to space dimension one, this method can be used for any space…
We study how the divide and conquer principle --- partition the available data into subsamples, compute an estimate from each subsample and combine these appropriately to form the final estimator --- works in non-standard problems where…
We show that the spaces of $A$-$m$-subharmonic and $B$-$m$-subharmonic functions differ in sufficently high dimensions. We also prove that the Monge-Amp\`ere type operator $\mathcal M_m$ associated to the space of $m$-plurisubharmonic…
We establish the equivalence between superharmonic functions and locally renormalized solutions for the elliptic measure data problems with $(p, q)$-growth. By showing that locally renormalized solutions are essentially bounded below and…
In this paper we discuss an extension of Perelman's comparison for quadrangles. Among applications of this new comparison theorem, we study the equidistance evolution of hypersurfaces in Alexandrov spaces with non-negative curvature. We…
Regula Falsi, or the method of false position, is a numerical method for finding an approximate solution to f(x) = 0 on a finite interval [a, b], where f is a real-valued continuous function on [a, b] and satisfies f(a)f(b) < 0. Previous…
We prove the convergence case of Khintchine's theorem, with general approximation functions that are not necessarily monotonic, for analytic nonplanar manifolds over local fields of positive characteristic. Our approach is based on the…
By using the well-known mountain pass theorem and Ekeland's variational principle, we prove that there exist at least two fully-non-trivial solutions for a $(p,q)$-Kirchhoff elliptic system with the Dirichlet boundary conditions and…
The proof of the Heisenberg uncertainty relation is modified to produce two improvements: (a) the resulting inequality is stronger because it includes the covariance between the two observables, and (b) the proof lifts certain restrictions…
A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under suitable assumptions. It is shown that the discrepancy…
The standard Bayesian model formalism comparison cannot be applied to most cosmological models as they lack well-motivated parameter priors. However, if the data-set being used is separable then it is possible to use some of the data to…
This paper deals with some inequalities for trigonometric and hyperbolic functions such as the Jordan inequality and its generalizations. In particular, lower and upper bounds for functions such as (sin x)/x and x/(sinh x) are proved.
This paper extends the self-improvement result of Keith and Zhong in [16] to the two-measure case. Our main result shows that a two-measure $(p,p)$-Poincar\'e inequality for $1<p<\infty$ improves to a $(p,p-\varepsilon)$-Poincar\'e…
We provide symmetrization results in the form of mass concentration comparisons for fractional singular elliptic equations in bounded domains, coupled with homogeneous external Dirichlet conditions. Two types of comparison results are…