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- W2962961528 abstract "In this note, we study the boundary regularity of the minimizers of a family of weak anchoring energies that model the states of liquid crystals. We establish optimal boundary regularity in all dimensions n≥3. In dimension n=3, this yields full regularity at the boundary, which stands in sharp contrast with the observation of boundary defects in physics works. We also show that, in the cases of weak and strong anchoring, the regularity of the minimizers is inherited from that of their corresponding limit problems. Dans cette note, nous étudions la régularité au bord des minimiseurs d'une famille d'énergies avec ancrage faible utilisée dans la modélisation des cristaux liquides. Nous établissons la régularité au bord optimale en toute dimension supérieure à 3. En dimension n=3, de tels minimiseurs sont lisses près du bord, ce qui va à l'encontre des observations de défauts sur le bord dans les travaux physiques. Nous montrons également que, dans les cas de faible et de fort ancrage, la régularité des minimiseurs est héritée de la régularité des minimiseurs des problèmes limites correspondants." @default.
- W2962961528 created "2019-07-30" @default.
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- W2962961528 date "2015-12-01" @default.
- W2962961528 modified "2023-10-18" @default.
- W2962961528 title "Boundary regularity of weakly anchored harmonic maps" @default.
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- W2962961528 doi "https://doi.org/10.1016/j.crma.2015.09.014" @default.
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