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On uniqueness of Frankl-Morawetz problem in ℝ2

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Abstract

For the equation

$$L[u]: = K(y)u_{xx} + u_{yy} + r(x,y)u = f(x,y)$$

(K (y)⪋0 whenevery⪋0) inG, bounded by a piecewise smooth curveΓ 0 fory>0 which intersects the liney=0 at the pointsA(−1, 0) andB(1, 0) and fory<0 by a smooth curveΓ 1 throughA which meets the characteristic of (1) throughB at the pointP, the uniqueness of the Frankl-Morawetz problem is proved without assuming thatΓ 1 is monotone.

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References

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Authors and Affiliations

  1. Institute for Physical Science and Technology, University of Maryland, Maryland

    A. K. Aziz

  2. Fachbereich 3-Mathematik, Technische Universität Berlin, Straße des 17. Juni 135, D-1000, Berlin 12

    M. Schneider

Authors
  1. A. K. Aziz
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  2. M. Schneider
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Additional information

Research supported in part by the U. S. Energy Research and Development Administration under Contract ERDA E (40-1) 3443.

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Aziz, A.K., Schneider, M. On uniqueness of Frankl-Morawetz problem in ℝ2 . Monatshefte für Mathematik 85, 265–276 (1978). https://doi.org/10.1007/BF01305956

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