Nabil Chems Eddine

Anisotropic variable exponent Sobolev spaces and applications to elliptic equations with critical growth

Abstract We establish critical embeddings for anisotropic Sobolev spaces with variable exponents, resolving, under log-Hölder continuity supplemented by finite Sobolev regularity and a quantitative integrability-gap condition, an open problem raised by Fan. We derive a Poincaré-t...

A low-energy multiwell genus principle below a concentration–compactness threshold

We establish a windowed symmetric minimax principle for even C 1 functionals on real, separable, reflexive Banach spaces when Palais–Smale compactness is available at levels in ( 0 , Λ ⁎ ) . Using the Krasnosel'skii genus together with Benci's pseudo-index, we localize the comple...