Related papers: An extremal problem for generalized Lelong numbers
We present a unified description of extremal metrics for the Laplace and Steklov eigenvalues on manifolds of arbitrary dimension using the notion of $n$-harmonic maps. Our approach extends the well-known results linking extremal metrics for…
We re-consider Leadbetter's extremal index for stationary sequences. It has interpretation as reciprocal of the expected size of an extremal cluster above high thresholds. We focus on heavy-tailed time series, in particular on regularly…
We consider a class of singular weighted anisotropic $p$-Laplace equations. We provide sufficient condition on the weight function that may vanish or blow up near the origin to ensure the existence of at least one weak solution in the…
A new numerical method for an inverse problem for an elliptic equation with unknown potential is proposed. In this problem the point source is running along a straight line and the source-dependent Dirichlet boundary condition is measured…
Each extreme edge of the Newton diagram of a plurisubharmonic polynomial on $\mathbb{C}^2$ gives rise to a plurisubharmonic polynomial. It is tempting to believe that the union of the extreme edges or the convex hull of said union will do…
We consider an elliptic system with regular H{\"o}lderian weight and exponential nonlinearity or with weight and boundary singularity, and, Dirichlet condition. We prove the boundedness of the volume of the solutions to those systems on the…
In this article, after recalling and discussing the conventional extremality, local extremality, stationarity and approximate stationarity properties of collections of sets and the corresponding (extended) extremal principle, we focus on…
In this paper, we investigate the extremal functions for anisotropic Trudinger-Moser inequalities. Our method uses convex symmetrization, the continuity of the supremum function, together with the relation between the supremums of the…
We extend holomorphically polyharmonic functions on a real ball to a complex set being the union of rotated balls. We solve a Dirichlet type problem for complex polyharmonic functions with the boundary condition given on the union of…
For a linear differential equation with a mild condition on its singularities, we discuss generalized continued fractions converging to expressions in its solutions and their derivatives. In the case of an order two linear differential…
Uniform bounds are obtained using the auxiliary Monge-Amp\`ere equation method for solutions of very general classes of fully non-linear partial differential equations, assuming the existence of a ${C}$-subsolution in the sense of G.…
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…
The existence of multiple nonnegative solutions to the anisotropic critical problem - \sum_{i=1}^{N} \frac{\partial}{\partial x_i} (| \frac{\partial u}{\partial x_i} |^{p_i-2} \frac{\partial u}{\partial x_i}) = |u|^{p^*-2} u {in}…
In this paper, we consider the problem of finding geodesics in a series of left-invariant problems endowed with sub-Lorentzian and Finsler structures. Explicit formulas for extremals are obtained in terms of convex trigonometric functions.…
We investigate some extremal problems in Fourier analysis and their connection to a problem in prime number theory. In particular, we improve the current bounds for the largest possible gap between consecutive primes assuming the Riemann…
The aim of this paper is investigating the existence of solutions of some semilinear elliptic problems on open bounded domains when the nonlinearity is subcritical and asymptotically linear at infinity and there is a perturbation term which…
The goal of the paper is to study a spectral problem corresponding to the mixed problem for a sixth order weak parabolic equation.
On a finite graph with a chosen partition of the vertex set into interior and boundary vertices, a $\lambda$-polyharmonic function is a complex function $f$ on the vertex set which satisfies $(\lambda \cdot I - P)^n f(x) = 0$ at each…
The core arguments used in various proofs of the extremal principle and its extensions as well as in primal and dual characterizations of approximate stationarity and transversality of collections of sets are exposed, analyzed and refined,…
We consider a time-fractional parabolic equation of doubly nonlinear type, featuring nonlinear terms both inside and outside the differential operator in time. The main nonlinearities are maximal monotone graphs, without restrictions on the…