An optimal Poincaré inequality for convex domains

@article{Payne1960AnOP,
  title={An optimal Poincar{\'e} inequality for convex domains},
  author={Lawrence Edward Payne and Hans F. Weinberger},
  journal={Archive for Rational Mechanics and Analysis},
  year={1960},
  volume={5},
  pages={286-292}
}

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References

SHOWING 1-7 OF 7 REFERENCES

Methoden der mathematischen Physik

VIII uber den Inhalt im einzelnen unterrichtet das ausfuhrliche Ver zeichnis. Zur Form ist etwas Grundsatzliches zu sagen: Das klassische Ideal einer gewissermassen atomistischen Auffassung der

Lower Bounds for Vibration Frequencies of Elastically Supported Membranes and Plates

If R is two-dimensional, the eigenvalues Xi(k) are proportional to the squares of the frequencies of a membrane covering R and elastically supported on the boundary B. If R is three-dimensional they

New bounds for solutions of second order elliptic partial differential equations

1. Introduction In a previous paper [10] the authors presented methods for determining, with arbitrary and known accuracy, the Dirichlet integral and the value at a point of a solution of Laplace's