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Ein schiefes Randwertproblem zu einer elliptischen Differentialgleichung zweiter Ordnung mit einer expliziten L 2 ‐Abschätzung für die zweiten Ableitungen der Lösung
Author(s) -
Witsch K. J.,
Leis R.
Publication year - 1979
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670010207
Subject(s) - mathematics , bounded function , domain (mathematical analysis) , boundary value problem , star (game theory) , geodetic datum , mathematical analysis , boundary (topology) , fredholm integral equation , integral equation , cartography , geography
In connection with the free boundary value problem of determining the earth's surface from measurements of gravitational potential and force‐field (“the geodetic boundary problem”), an oblique derivative problemarises, where D 0 is some bounded domain, star shaped with respect to the origin. In order to prove a uniquencess theorem for the geodetic boundary problem, it is essential to give estimates for (weighted) L 2 ‐norms of the second derivatives of the solutions so that their bounds can be estimated numerically if bounds for the function describing the boundary are known. In this paper a Fredholm inverse for the above problem is constructed and the second derivatives of the solutions are estimated in the desired form.