Results 61 to 70 of about 13,900 (197)
Fractional Dirichlet problems with an overdetermined non‐local Neumann condition
Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.Abstract We investigate symmetry and quantitative approximate symmetry for an overdetermined problem related to the fractional torsion equation in a regular open, bounded set Ω⊆Rn$\Omega \subseteq \mathbb {R}^n$. Specifically, we show that if Ω¯$\overline{\Omega }$ has positive reach and the non‐local normal derivative introduced in Dipierro, Ros‐Oton ...
Michele Gatti +2 more
wiley +1 more source
A Liouville theorem for ancient solutions to a semilinear heat equation and its elliptic counterpart
, 2020 We establish the nonexistence of nontrivial ancient solutions to the nonlinear heat equation $u_t=\Delta u+|u|^{p-1}u$ which are smaller in absolute value than the self-similar radial singular steady state, provided that the exponent $p$ is strictly ...
Sourdis, Christos
core
Mathematical Methods in the Applied Sciences, Volume 49, Issue 4, Page 2135-2160, 15 March 2026.ABSTRACT It is an elementary fact in the scientific literature that the Lipschitz norm of the realization function of a feedforward fully connected rectified linear unit (ReLU) artificial neural network (ANN) can, up to a multiplicative constant, be bounded from above by sums of powers of the norm of the ANN parameter vector.
Arnulf Jentzen, Timo Kröger
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Existence of solutions for p-Kirchhoff type problems with critical exponent
Electronic Journal of Differential Equations, 2011 We study the existence of solutions for the p-Kirchhoff type problem involving the critical Sobolev exponent, $$displaylines{ -Big[gBig(int_Omega|abla u|^pdxBig)Big]Delta_pu =lambda f(x,u)+|u|^{p^star-2}uquadext{in }Omega,cr u=0quadext{on ...
Ahmed Hamydy +2 more
doaj
Sobolev and isoperimetric inequalities with monomial weights [PDF]
, 2015 We consider the monomial weight $|x_1|^{A_1}...|x_n|^{A_n}$ in $\mathbb R^n$, where $A_i\geq0$ is a real number for each $i=1,...,n$, and establish Sobolev, isoperimetric, Morrey, and Trudinger inequalities involving this weight. They are the analogue of
Cabre, Xavier, Ros-Oton, Xavier
core
On elliptic systems with Sobolev critical exponent
Discrete and Continuous Dynamical Systems, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +3 more sources
Breaking Barriers in High‐Order Spectral Methods: The Intrinsic Matrix Approach
International Journal for Numerical Methods in Engineering, Volume 127, Issue 5, 15 March 2026.ABSTRACT This paper introduces a unified framework in Hilbert spaces for applying high‐order differential operators in bounded domains using Chebyshev, Legendre, and Fourier spectral methods. By exploiting the banded structure of differentiation matrices and embedding boundary conditions directly into the operator through a scaling law relating ...
Osvaldo Guimarães, José R. C. Piqueira
wiley +1 more source
Boundary Value Problems, 2019 In this paper, we study a fractional Kirchhoff type equation with Hardy–Littlewood–Sobolev critical exponent. By using variational methods, we obtain the existence of mountain-pass type solution and negative energy solutions.
Jichao Wang, Jian Zhang, Yujun Cui
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Sign Changing Solutions for Coupled Critical Elliptic Equations
Journal of Function Spaces, 2020 In this paper, we consider the coupled elliptic system with a Sobolev critical exponent.
Xin Wang, Xiaorui Yue
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Generalized quasi‐geostrophic equation in critical Lorentz–Besov spaces, based on maximal regularity
Mathematische Nachrichten, Volume 299, Issue 3, Page 637-660, March 2026.Abstract We consider the quasi‐geostrophic equation with its principal part (−Δ)α${(-\mathrm{\Delta})^{\alpha}}$ for α>1/2$\alpha >1/2$ in Rn$\mathbb {R}^n$ with n≥2$n \ge 2$. We show that for every initial data θ0∈Ḃr,q1−2α+nr$\theta _0 \in \dot{B}^{1-2\alpha + \frac{n}{r}}_{r, q}$ with 1
Hideo Kozono +2 more
wiley +1 more source