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Best constant in Sobolev inequality.(English)Zbl 0353.46018


MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
28A75 Length, area, volume, other geometric measure theory
26D10 Inequalities involving derivatives and differential and integral operators
49Q20 Variational problems in a geometric measure-theoretic setting
52A40 Inequalities and extremum problems involving convexity in convex geometry
49Q15 Geometric measure and integration theory, integral and normal currents in optimization

Cite

References:

[1]L. Bers - F. John - M. Schechter,Partial Differential Equations, Interscience (1964)
[2]G. A. Bliss,An integral inequality, Journal London Math. Soc.,5 (1930). ·JFM 56.0434.02
[3]H. Federer,Curvature measure, Trans. Amer. Math. Soc.,93 (1959). ·Zbl 0089.38402
[4]H. Federer - W. Fleming,Normal and integral currents, Annals of Math.,72 (1960). ·Zbl 0187.31301
[5]W. Fleming,Functions whose partial derivatives are measures, Illinois J. Math.,4 (1960). ·Zbl 0151.05402
[6]W. Fleming - R. Rishel,An integral formula for total gradient variation, Arch. Math.,11 (1960). ·Zbl 0094.26301
[7]M. Miranda,Distribuzioni aventi derivate misure, Ann. Scuola Norm. Sup. Pisa,18 (1964). ·Zbl 0131.11802
[8]M. Miranda,Sul minimo dell’integrale del gradiente di una funzione, Ann. Scuola Norm. Sup. Pisa,19 (1965).
[9]M. Miranda,Disuguaglianze di Sobolev sulle ipersuperfici minimali, Rend. Sem. Mat. Univ. Padova,38 (1967). ·Zbl 0175.11802
[10]G. Rosen,Minimum value for c in the Sobolev inequality, SIAM J. Appl. Math.,21 (1971). ·Zbl 0201.38704
[11]S. L. Sobolev,On a theorem of functional analysis (in russian), Mat. Sb.,4 (1938).
[12]S. L. Sobolev,Applications of functional analysis in mathematical physics, Amer. Math. Soc. (1963). ·Zbl 0123.09003
[13]L. C. Young,Partial area, Rivista Mat. Univ. Parma,10 (1959).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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