[كتاب][B] Blow-up theory for elliptic PDEs in Riemannian geometry

O Druet, E Hebey, F Robert - 2009‏ - books.google.com
Elliptic equations of critical Sobolev growth have been the target of investigation for decades
because they have proved to be of great importance in analysis, geometry, and physics. The …

Sobolev inequalities for the Hardy–Schrödinger operator: extremals and critical dimensions

N Ghoussoub, F Robert - Bulletin of Mathematical Sciences, 2016‏ - Springer
In this survey paper, we consider variational problems involving the Hardy–Schrödinger
operator L_ γ:=-Δ-γ| x|^ 2 L γ:=-Δ-γ| x| 2 on a smooth domain Ω Ω of R^ n R n with 0 ∈ Ω 0∈ …

[كتاب][B] Functional Inequalities: New Perspectives and New Applications: New Perspectives and New Applications

N Ghoussoub, A Moradifam - 2013‏ - books.google.com
" The book describes how functional inequalities are often manifestations of natural
mathematical structures and physical phenomena, and how a few general principles …

Normalized solutions to p-Laplacian equations with combined nonlinearities

Z Zhang, Z Zhang - Nonlinearity, 2022‏ - iopscience.iop.org
In this paper, we study the p-Laplacian equation with a L p-norm constraint: $\begin {cases}-
{{\Delta}} _ {p} u=\lambda\vert u {\vert}^{p-2} u+\mu\vert u {\vert}^{q-2} u+ g (u)\quad\text …

Solutions for semilinear elliptic equations with critical exponents and Hardy potential

D Cao, P Han - Journal of Differential Equations, 2004‏ - Elsevier
In this paper, we answer affirmatively an open problem (cf. Theorem 4′ in Ferrero and
Gazzola (J. Differential Equations 177 (2001) 494): Let Ω∋ 0 be an open-bounded domain …

[HTML][HTML] A note on the sign-changing solutions to elliptic problems with critical Sobolev and Hardy terms

D Cao, S Peng - Journal of Differential Equations, 2003‏ - Elsevier
A note on the sign-changing solutions to elliptic problems with critical Sobolev and Hardy
terms - ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books …

[PDF][PDF] Solutions for p (x)-Laplacian Dirichlet problems with singular coefficients

X Fan - Journal of Mathematical Analysis and applications, 2005‏ - core.ac.uk
Solutions for p(x)-Laplacian Dirichlet problems with singular coefficients Page 1 J. Math. Anal.
Appl. 312 (2005) 464–477 www.elsevier.com/locate/jmaa Solutions for p(x)-Laplacian Dirichlet …

The Allen–Cahn equation on closed manifolds

P Gaspar, MAM Guaraco - Calculus of Variations and Partial Differential …, 2018‏ - Springer
We study global variational properties of the space of solutions to-ε^ 2 Δ u+ W'(u)= 0-ε 2 Δ u+
W′(u)= 0 on any closed Riemannian manifold M. Our techniques are inspired by recent …

Hardy–Sobolev critical elliptic equations with boundary singularities

N Ghoussoub, XS Kang - Annales de l'Institut Henri Poincaré C, Analyse …, 2004‏ - Elsevier
Unlike the non-singular case s= 0, or the case when 0 belongs to the interior of a domain Ω
in R n (n⩾ 3), we show that the value and the attainability of the best Hardy–Sobolev …

The effect of curvature on the best constant in the Hardy–Sobolev inequalities

N Ghoussoub, F Robert - Geometric & Functional Analysis GAFA, 2006‏ - Springer
We address the question of attainability of the best constant in the following Hardy–Sobolev
inequality on a smooth domain Ω of R^ n:\mu_s (Ω):= inf\left {\int_ Ω| ∇ u|^ 2 dx; u ∈ H_ 1 …