Results 61 to 70 of about 410 (182)

Function spaces for decoupling

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract We introduce new function spaces LW,sq,p(Rn)$\mathcal {L}_{W,s}^{q,p}(\mathbb {R}^{n})$ that yield a natural reformulation of the ℓqLp$\ell ^{q}L^{p}$ decoupling inequalities for the sphere and the light cone. These spaces are invariant under the Euclidean half‐wave propagators, but not under all Fourier integral operators unless p=q$p=q$, in ...
Andrew Hassell, Pierre Portal, Jan Rozendaal, Po‐Lam Yung   +3 more
wiley   +1 more source

On elliptic systems with Sobolev critical exponent

Discrete and Continuous Dynamical Systems, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +3 more sources

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, Julian Scheuer, Tobias Weth   +2 more
wiley   +1 more source

Existence results for elliptic systems involving critical Sobolev exponents

Electronic Journal of Differential Equations, 2004
n this paper, we study the existence and nonexistence of positive solutions of an elliptic system involving critical Sobolev exponent perturbed by a weakly coupled term.
Mohammed Bouchekif, Yasmina Nasri
doaj  

Existence and multiplicity of positive solutions for Kirchhoff type equations at the critical frequency

Electronic Journal of Qualitative Theory of Differential Equations
We consider the following Kirchhoff equation with critical Sobolev exponent \begin{equation}\label{eq0} \begin{cases} \left(a+b\displaystyle\int_{\mathbb{R}^{N}}|(-\Delta)^{\frac{s}{2}}u|^{2}dx\right)(-\Delta)^{s}u=|u|^{2^{*}_{s}-2}u+\mu g(x), \quad ...
Juhua He, Sijian You
doaj   +1 more source

A note on problems involving critical Sobolev exponents

Differential and Integral Equations, 1995
Existence of a nontrivial solution of the semilinear elliptic equation \(- \Delta u= | u|^{p-2} u+ f(x,u)\) in \(G\), \(u=0\) on \(\partial G\) is shown in this paper. Here \(G\) denotes a smooth bounded domain in \(\mathbb{R}^ N\) \((N\geq 4)\), \(p-1= (N+2)/ (N-2)\) (the so-called critical Sobolev exponent) and \(f(x,u)= \lambda u+ g(x,u)\) is ...
Costa, D. G., Silva, E. A.
openaire   +3 more sources

Infinitely many positive solutions for p-Laplacian equations with singular and critical growth terms

Boundary Value Problems
In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p-Laplacian type involving a singularity and a critical Sobolev exponent { − Δ p u = u p ∗ − 1 + λ | u | γ − 1 u , in Ω , u = 0 , on ∂ Ω ...
Chen-Xi Wang, Hong-Min Suo
doaj   +1 more source

On Dirac equation with a potential and critical Sobolev exponent

Communications on Pure and Applied Analysis, 2015
The authors consider a Dirac equation with a nonlinear zero order term and additional potential on a closed spin manifold. The nonlinearity is critical in the sense of Sobolev embedding -- analogously to the nonlinearity of the Yamabe equation. They prove existence of solutions under some mild assumption on the spectrum of the Dirac operator with ...
Gong, Wenmin, Lu, Guangcun
openaire   +2 more sources

Non-homogeneous problem for fractional Laplacian involving critical Sobolev exponent

Electronic Journal of Differential Equations, 2017
In this article, we study the existence of positive solutions for the nonhomogeneous fractional equation involving critical Sobolev exponent $$\displaylines{ (-\Delta)^{s} u +\lambda u=u^p+\mu f(x), \quad u>0\quad \text{in } \Omega,\cr u =0, \quad \
Kun Cheng, Li Wang
doaj