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On the Agmon-Miranda maximum principle for solutions of elliptic equations in polyhedral and polygonal domains

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References

  1. Agmon, S.: Maximum theorems for solutions of higher order elliptic equations. Bull. Amer. Math. Soc. 66 (1960), 77–80.

    Google Scholar 

  2. Agranovič, M. S., and M. I. Višik: Elliptic problems with parameter and parabolic problems of general type. Uspekhi Mat. Nauk 19 (1964) 3, 53–161 (Russian).

    Google Scholar 

  3. Albinus, G.: Estimates of Agmon-Miranda type for solutions of the Dirichlet problem for linear differential operators of order 2min plane domains with corners. Preprint, Akad. der Wiss. der DDR, Inst. für Math., Berlin 1981.

    Google Scholar 

  4. Dauge, M.: Elliptic boundary value problems on corner domains. Berlin-Heidelberg-New York-London-Paris-Tokyo: Springer-Verlag 1988.

    Google Scholar 

  5. Gochberg, I. Z., and E. I. Sigal: Operator generalization of the theorem on the logarithmic residue and the Rouché theorem. Mat. Sb. 84 (1971) 4, 607–629 (Russian).

    Google Scholar 

  6. Grisvard: Elliptic problems in non-smooth domains. London: Pitman 1985.

    Google Scholar 

  7. Kondratjev, V. A.: Boundary value problems for elliptic equations in domains with conical or angular points. Trudy Moskov. Mat. Ob. 16 (1967), 209–292 (Russian).

    Google Scholar 

  8. Kondratjev, V. A.: On the smoothness of the solution of the Dirichlet problem for second order elliptic equations in a piecewise smooth domain. Differents. Uravn. 6 (1970) 10, 1831–1843 (Russian).

    Google Scholar 

  9. Koslov, V. A., and V. G. Maz'ya: Spectral properties of operator pencils generated by elliptic boundary value problems in a cone. Funktional. Analis i Prilozhen. 22 (1988) 2, 38–46. (Russian).

    Google Scholar 

  10. Krasovskij, Ju. P.: Estimates of the growth of the derivatives of solutions of homogeneous elliptic equations near the boundary. Dokl. Akad. Nauk SSSR 184 (1969) 3, 534–537 (Russian).

    Google Scholar 

  11. Maz'ya, V. G., and B. A. Plamenevskij: Elliptic boundary value problems on manifolds with singularities. Probl. Mat. Anal. 6 (1977), 85–142 (Russian).

    Google Scholar 

  12. Maz'ya, V. G., and B. A. Plamenevskij: On the coefficients in the asymptotics of solutions of elliptic boundary value problems in domains with conical points. Math. Nachr. 76 (1977), 29–60 (Russian).

    Google Scholar 

  13. Maz'ya, V. G., and B. A. Plamenevskij: Estimates in L p and Hölder classes and the Agmon-Miranda maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary. Math. Nachr. 81 (1978), 25–82 (Russian).

    Google Scholar 

  14. Maz'ya, V. G., and B. A: Plamenevskij: L p-estimates for solutions of elliptic boundary value problems in domains with edges. Trudy Moskov. Mat. Obshch. 37 (1978), 49–93 (Russian).

    Google Scholar 

  15. Maz'ya, V. G., and B. A. Plamenevskij: Estimates of the Green function and Schauder estimates of solutions of elliptic boundary value problems in a dihedral angle. Sibirsk. Mat. <Z. 19 (1978) 5, 1065–1083 (Russian).

    Google Scholar 

  16. Maz'ya, V. G., and B. A. Plamenevskij: On the asymptotics of the fundamental solutions of elliptic boundary value problems in domains with conical points. Probl. Mat. Anal. 7 (1979), 100–145 (Russian).

    Google Scholar 

  17. Maz'ya, V. G., and B. A. Plamenevskij:On the maximum principle for the biharmonic equation in a domain with conical points. Izv. Vyssh. Uchebn. Zaved. 2 (1981), 52–59 (Russian).

    Google Scholar 

  18. Maz'ya, V. G., and B. A. Plamenevskij: The first boundary value problem for elliptic equations in the mathematical physics in domains with piecewise smooth boundaries. I: Z. Anal. Anwendungen 2 (1983) 4, 335–359; II: Izv. Vyssh. Uchebn. Zaved. 2 (1983) 6, 523–551 (Russian).

    Google Scholar 

  19. Maz'ya, V. G.: Nazarov, S. A.; Plamenevskij, B. A.: On the singularities of the solutions of the Dirichlet problem in the exterior of a slender cone. Mat. Sb. 122 (1983) 4, 435–457 (Russian).

    Google Scholar 

  20. Maz'ya, V. G., and J. Rossmann: Über die Lösbarkeit und die Asymptotik der Lösungen elliptischer Randwertaufgaben in Gebieten mit Kanten III. Preprint 31/84, Akad. der Wiss. der DDR, Inst. für Math., Berlin 1984.

  21. Maz'ya, V. G., and J. Rossmann: Über die Asymptotik der Lösungen elliptischer Randwertaufgaben in der Umgebung von Kanten. Math. Nachr. 138 (1988), 27–53.

    Google Scholar 

  22. Maz'ya, V. G., and J. Rossmann: On the Agmon-Miranda maximum principle for solutions of elliptic equations in domains of R n with conical points. To appear.

  23. Miranda, C.: Formule die maggiorazione e teorema di esistenza per le fuzioni biarmoniche in due variabili. Giorn. Math. Battaglini 78 (1949), 97–118.

    Google Scholar 

  24. Miranda, C.: Teorema del massimo modulo u teorema di esistenza e di unicita per il problema Dirichlet relative alle equazioni ellitiche in due variabili. Ann. Mat. Pura Appl. 46 (1958), 265–311.

    Google Scholar 

  25. Rempel, S. and B.-W. Schulze: Asymptotics for elliptic mixed boundary value problems. Berlin: Akademie-Verlag 1989.

    Google Scholar 

  26. Sändig, A.-M.: Das Maximum-Prinzip vom Miranda-Agmon-Typ für Lösungen der biharmonischen Gleichung in einem R Rechteck. Math. Nachr. 96 (1980), 49–51.

    Google Scholar 

  27. Schulze, B.-W.: On a-priori estimates in maximum norms for strongly elliptic systems. Sibirsk. Mat. <Z. 16 (1975) 2, 384–394 (Russian).

    Google Scholar 

  28. Schulze, B.-W.: Abschätzungen in Normen gleichmäßiger Konvergenz für elliptische Randwertprobleme. Math. Nachr. 67 (1975), 303–315.

    Google Scholar 

  29. Schulze, B.-W.: Ellipticity and continuous conormal asymptotics on manifolds with conical singularities. Math. Nachr. 136 (1988), 7–57.

    Google Scholar 

  30. Schulze, B.-W.: Regularity with continuous and branching asymptotics for elliptic operators on manifolds with edges. Integral Equations Operator Theory 11 (1988), 557–602.

    Google Scholar 

  31. Schulze, B.-W., and G. Wildenhain: Methoden der Potentialtheorie für elliptische Differentialgleichungen beliebiger Ordnung. Berlin: Akademie-Verlag 1977.

    Google Scholar 

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Mazýa, V.G., Rossmann, J. On the Agmon-Miranda maximum principle for solutions of elliptic equations in polyhedral and polygonal domains. Ann Glob Anal Geom 9, 253–303 (1991). https://doi.org/10.1007/BF00136815

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