The free boundary for semilinear problems with highly oscillating singular terms
Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.Abstract We investigate general semilinear (obstacle‐like) problems of the form Δu=f(u)$\Delta u = f(u)$, where f(u)$f(u)$ has a singularity/jump at {u=0}$\lbrace u=0\rbrace$ giving rise to a free boundary. Unlike many works on such equations where f$f$ is approximately homogeneous near {u=0}$\lbrace u = 0\rbrace$, we work under assumptions allowing ...
Mark Allen +2 more
wiley +1 more source
Estimates for smooth Weyl sums on minor arcs
Bulletin of the London Mathematical Society, Volume 57, Issue 3, Page 657-668, March 2025.Abstract We provide new estimates for smooth Weyl sums on minor arcs and explore their consequences for the distribution of the fractional parts of αnk$\alpha n^k$. In particular, when k⩾6$k\geqslant 6$ and ρ(k)$\rho (k)$ is defined via the relation ρ(k)−1=k(logk+8.02113)$\rho (k)^{-1}=k(\log k+8.02113)$, then for all large numbers N$N$ there is an ...
Jörg Brüdern, Trevor D. Wooley
wiley +1 more source
The singular series of a cubic form in many variables and a new proof of Davenport's Shrinking Lemma
Bulletin of the London Mathematical Society, Volume 57, Issue 3, Page 681-691, March 2025.Abstract We study the singular series associated to a cubic form with integer coefficients. If the number of variables is at least 10, we prove the absolute convergence (and hence positivity) under the assumption of Davenport's Geometric Condition, improving on a result of Heath‐Brown. For the case of nine variables, we give a conditional treatment. We
Christian Bernert
wiley +1 more source
Ergodic averages along sequences of slow growth
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract We consider pointwise almost everywhere convergence of weighted ergodic averages along the sequence Ω(n)$ \Omega (n)$, where Ω(n)$ \Omega (n)$ denotes the number of prime factors of n$ n$ counted with multiplicities. It was previously shown that a pointwise ergodic theorem for L∞$L^\infty$ functions does not hold along Ω(n)$ \Omega (n)$.
Kaitlyn Loyd, Sovanlal Mondal
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Persistence of the solution to the Euler equations in an end‐point critical Triebel–Lizorkin space
Mathematical Methods in the Applied Sciences, Volume 48, Issue 2, Page 2421-2433, 30 January 2025.Local stay of the solutions to the Euler equations for an ideal incompressible fluid in the end‐point Triebel–Lizorkin space F1,∞sℝd$$ {F}_{1,\infty}^s\left({\mathbb{R}}^d\right) $$ with s≥d+1$$ s\ge d+1 $$ is clarified.
JunSeok Hwang, Hee Chul Pak
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Calderón–Zygmund theory on some Lie groups of exponential growth
Mathematische Nachrichten, Volume 298, Issue 1, Page 113-141, January 2025.Abstract Let G=N⋊A$G = N \rtimes A$, where N$N$ is a stratified Lie group and A=R+$A= \mathbb {R}_+$ acts on N$N$ via automorphic dilations. We prove that the group G$G$ has the Calderón–Zygmund property, in the sense of Hebisch and Steger, with respect to a family of flow measures and metrics.
Filippo De Mari +3 more
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The Real and Complex Techniques in Harmonic Analysis from the Point of View of Covariant Transform
, 2014 This note reviews complex and real techniques in harmonic analysis. We describe a common source of both approaches rooted in the covariant transform generated by the affine group.
Kisil, Vladimir V.
core
Effective upper bounds on the number of resonances in potential scattering
Mathematika, Volume 71, Issue 1, January 2025.Abstract We prove upper bounds on the number of resonances and eigenvalues of Schrödinger operators −Δ+V$-\Delta +V$ with complex‐valued potentials, where d⩾3$d\geqslant 3$ is odd. The novel feature of our upper bounds is that they are effective, in the sense that they only depend on an exponentially weighted norm of V.
Jean‐Claude Cuenin
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Uniform Treatment of Integral Majorization Inequalities with Applications to Hermite-Hadamard-Fejér-Type Inequalities and f-Divergences. [PDF]
Entropy (Basel), 2023 Horváth L.
europepmc +1 more source
Finite-time and fixed-time stabilization of multiple memristive neural networks with nonlinear coupling. [PDF]
Cogn Neurodyn, 2022 Yang C, Liu Y, Huang L.
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