most citedImproved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces

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math.AP2019

Torus-like solutions for the Landau-de Gennes model. Part I: the Lyuksyutov regime

Federico Dipasquale, Vincent Millot, Adriano Pisante

We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains. Assuming smooth and uniaxial (e.g. homeotrop…

math.AP2013★ 4 cited

Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces

Giampiero Palatucci, Adriano Pisante

We obtain an improved Sobolev inequality in H^s spaces involving Morrey norms. This refinement yields a direct proof of the existence of optimizers and the compactness up to symmet…