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Abstract In this paper, we establish the classical Hardy inequality in the solid torus and some variants of it. The general idea is to use the fact that Sobolev embeddings… Click to show full abstract
Abstract In this paper, we establish the classical Hardy inequality in the solid torus and some variants of it. The general idea is to use the fact that Sobolev embeddings can be improved in the presence of symmetries. In all cases, using techniques that exploit the symmetry presented by the solid torus, we calculate the displayed best constants and we prove that they are the same as the standard Hardy best constants which appear in convex domains although the solid torus is not convex.
Keywords:
inequalities solid;
sharp hardy;
torus;
solid torus;
hardy inequalities
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2017
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Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!