In this paper, we concern the isolated singular solutions for Lane–Emden equations involving the CKN operator
In this paper, we concern the isolated singular solutions for Lane–Emden equations involving the CKN operator
We prove that an aggregate Toeplitz operator on the Fréchet space of all entire functions is a Fredholm operator if and only if its symbol does not vanish. The result is motivated by and closely resembles the classical result of Gohberg and Douglas from the Hardy space theory of Toeplitz operators. There are however some subtle differences which we also discuss.
In this paper, we describe orbits of the automorphism group on an affine horospherical variety in terms of degrees of homogeneous with respect to natural grading locally nilpotent derivations. In case of (possibly nonnormal) toric varieties, a description of orbits of the automorphism group in terms of corresponding weight monoid is obtained.
Conditions for harmonic analysis in generalized Orlicz spaces have been studied over the past decade. One approach involves the generalized inverse of so-called weak -functions. It featured prominently in the monograph Orlicz Spaces and Generalized Orlicz Spaces [P. Harjulehto and P. Hästö, Lecture Notes in Mathematics, vol. 2236, Springer, Cham, 2019]. While generally successful, the inverse function formulation of the decay condition (A2) in the monograph contains a flaw, which we explain and correct in this note. We also present some new results related to the conditions, including a more general result for the density of smooth functions.
We study the regularity properties of Hölder continuous minimizers to non-autonomous functionals satisfying -growth conditions, under Besov assumptions on the coefficients. In particular, we are able to prove higher integrability and higher differentiability results for solutions to our minimum problem.
In this paper, we consider the parabolic–elliptic Keller–Segel system, which is coupled to the incompressible Navier–Stokes equations through transportation and friction. It is shown that when the system is diffused by Lévy motion, the well-posedness of the mild solution to the corresponding Cauchy problem in homogeneous Besov spaces is established by means of the Banach fixed point theorem. Furthermore, we prove the Lorentz regularity in time direction and the maximal regularity of solutions. In addition, we obtain the additional regularity and explore the time decay property of global mild solutions.
We provide a variant of Geršgorin's circle theorem, where the -estimates are swapped for -estimates, more suitable for the infinite-dimensional Hilbert space setting.
We characterize genus 3 complex smooth hyperelliptic curves that admit two additional involutions as curves that can be built from five points in with a distinguished triple. We are able to write down explicit equations for the curves and all their quotient curves. We show that, fixing one of the elliptic quotient curve, the Prym map becomes a 2:1 map and therefore the hyperelliptic Klein Prym map, constructed recently by the first author with A. Ortega, is also 2:1 in this case. As a by-product we show an explicit family of polarized abelian surfaces (for ), such that any surface in the family satisfying a certain explicit condition is abstractly non-isomorphic to its dual abelian surface.
In this paper, we present the result of global existence of solution for the wave equation with boundary variable damping term. Then, we prove that this global solution is stable. Our study is based on the semi-groups theory and some integral inequalities.
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