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Agmon, S.; Douglis, A.; Nirenberg, L.: Estimates near the boundary for elliptic partial differential equations satisfying general boundary conditions I. Comm. Pure Appl. Math. 12 (1959), 623–727.
Edmunds, D.E.; Kufner, A.; Rákosnik, J.: Embeddings of Sobolev spaces with weights of power type. Z. Anal. Anw. 4 (1985), 25–34.
Gilbarg, D.; Trudinger, N.S.: Elliptic partial differential equations of second order. Berlin, Heidelberg, New York: Springer 1977.
Heiskanen, W.A.; Moritz, H.: Physical geodesy. San Francisco, London: Freeman 1967.
Hörmander, L.: The boundary problems of physical geodesy. Arch. for Rational Mech. Anal. 63 (1976), 1–52.
Holota, P.: Boundary value problems in physical geodesy: present state, boundary perturbation and the Green-Stokes representation. Proc. of the 1st Hotine-Marussi Symposium on Mathematical Geodesy at Rome, 1985; ed..: F. Sansó, Istituto di Topografia, Fotogrammetria e Geofesica, Politecnico di Milano, Piazza Leonardo da Vinci 32: Milano 1986.
Kinderlehrer, D.; Nirenberg, L.: Regularity in free boundary problems. Ann. Scuola Norm. Sup. Pisa, Ser. IV, Vol. IV (1977), 373–391.
McOwen, R.C.: The behaviour of the Laplacian on weighted Sobolev Spaces. Comm. Pure Appl. Math. 32 (1979), 783–795.
Nirenberg, L.; Walker, H.F.: The null spaces of elliptic partial differential operators in IRn. J. Math. Anal. Appl. 42 (1973), 271–301.
Sansó, F.: The geodetic boundary value problem in gravity space. Atti Accad. Naz. Lincei Mem. Cl. Sci. Math. Natur. Sez. Ia, Ser. VIII, Vol. XIV (1977).
Sansó, F.: The local solvability of Molodensky’s problem in gravity space. Manuscripta Geodetica 3 (1978), 157–227.
Schechter, M.: On Lp estimates and regularity, I, Amer. J. Math. 85 (1963), 1–13.
Schechter, M.: Principles of functional analysis. New York: Academic Press 1971.
Stein, E.M.; Weiss, G.: Fractional integrals on n-dimensional Euclidean space. J. Math. Mech. 7 (4) (1958), 503–514.
Triebel, H.: A remark on a paper by D.F. Edmunds, A. Kufner and J. Rákosnik "Embedding of Sobolev spaces with weights of power type". Z. Anal. Anw. 4 (1985), 35–38.
Witsch, K.J.: Ein schiefes Randwertproblem zu einer elliptischen Differentialgleichung zweiter Ordnung mit einer expliziten L2-Abschätzung für die zweiten Ableitungen der Lösung. Math. Meth. in the Appl. Sci. 1 (1979), 214–240.
Witsch, K.J.: A uniqueness result for the geodetic boundary problem. J. Diff. Equ. 38 (1980), 104–125.
Witsch, K.J.: On a free boundary value problem of physical geodesy, I (Uniqueness). Math. Meth. in the Appl. Sci. 7 (1985), 269–289.
Witsch, K.J.: On a free boundary value problem of physical geodesy, II (Existence). Math. Meth. in the Appl. Sci. 8 (1986), 1–22.
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Witsch, K.J. (1988). On a modified version of the free geodetic boundary-value problem. In: Hildebrandt, S., Leis, R. (eds) Partial Differential Equations and Calculus of Variations. Lecture Notes in Mathematics, vol 1357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082877
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DOI: https://doi.org/10.1007/BFb0082877
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