On Wiener's type regularity of a boundary point for higher order elliptic equations

Maz'ya, Vladimir

  • Nonlinear Analysis, Function Spaces and Applications, Publisher: Czech Academy of Sciences, Mathematical Institute(Praha), page 119-155

How to cite

top

Maz'ya, Vladimir. "On Wiener's type regularity of a boundary point for higher order elliptic equations." Nonlinear Analysis, Function Spaces and Applications. Praha: Czech Academy of Sciences, Mathematical Institute, 1999. 119-155. <http://eudml.org/doc/221779>.

@inProceedings{Mazya1999,
author = {Maz'ya, Vladimir},
booktitle = {Nonlinear Analysis, Function Spaces and Applications},
keywords = {Spring school; Proceedings; Nonlinear analysis; Function spaces; Prague (Czech Republic)},
location = {Praha},
pages = {119-155},
publisher = {Czech Academy of Sciences, Mathematical Institute},
title = {On Wiener's type regularity of a boundary point for higher order elliptic equations},
url = {http://eudml.org/doc/221779},
year = {1999},
}

TY - CLSWK
AU - Maz'ya, Vladimir
TI - On Wiener's type regularity of a boundary point for higher order elliptic equations
T2 - Nonlinear Analysis, Function Spaces and Applications
PY - 1999
CY - Praha
PB - Czech Academy of Sciences, Mathematical Institute
SP - 119
EP - 155
KW - Spring school; Proceedings; Nonlinear analysis; Function spaces; Prague (Czech Republic)
UR - http://eudml.org/doc/221779
ER -

References

top
  1. Wiener N., The Dirichlet problem, J. Math. Phys. 3 (1924), 127–146. (1924) 
  2. Wiener N., Certain notions in potential theory, J. Math. Phys. 3 (1924), 24–51. (1924) 
  3. Poincaré H., Sur les équations aux derivées partielles de la physique mathématique, Amer. J. Math. 12 (1890), 211–299. MR1505534
  4. Zaremba S. C., Sur le principe du minimum, Bull. Acad.Sci. Cracovie, Juillet 1909. (1909) 
  5. Lebesgue H., Sur des cas d’impossibilité du problème de Dirichlet ordinaire, C. R. des Séances de la Société Mathématique de France 17 (1913). (1913) 
  6. Littman W., Stampacchia G., Weinberger H. F., Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa Serie III, 17 (1963), 43–77. (1963) Zbl0116.30302MR0161019
  7. Fabes E. G., Jerison D., Kenig C., The Wiener test for degenerate elliptic equations, Ann. Inst. Fourier (Grenoble) 32 (1982), 151–182. (1982) MR0688024
  8. Maso G. Dal, Mosco U., Wiener criteria and energy decay for relaxed Dirichlet problems, Arch. Rational Mech. Anal. 95 (1986), 345–387. (1986) MR0853783
  9. Maz’ya V. G., On the continuity at a boundary point of solutions of quasilinear elliptic equations, Vestnik Leningrad Univ., Mat. 3 (1976), 225–242; English transl.: Vestnik Leningrad Univ. 25 (1970), 42–55. (1976) MR0274948
  10. Gariepy R., Ziemer W. P., A regularity condition at the boundary for solutions of quasilinear elliptic equations, Arch. Rational Mech. Anal. 67 (1977), 25–39. (1977) Zbl0389.35023MR0492836
  11. Adams D. R., Hedberg L. I., Functions spaces and potential theory, Springer-Verlag, Berlin 1995. (1995) MR1411441
  12. Lindqvist P., Martio O., Two theorems of N. Wiener for solutions of quasilinear elliptic equations, Acta Math. 155 (1985), 153–171. (1985) Zbl0607.35042MR0806413
  13. Kilpeläinen T., Malý J., The Wiener test and potential estimates for quasilinear elliptic equations, Acta Math. 172 (1994), 137–161. (1994) 
  14. Malý J., Ziemer W. P., Regularity of solutions of elliptic partial differential equations, Mathematical Surveys and Monographs, vol. 51, American Mathematical Society, Providence, RI 1997. (1997) Zbl0882.35001MR1461542
  15. Maz’ya V. G., Sobolev spaces, Springer-Verlag, Berlin 1985. (1985) Zbl0727.46017MR0817985
  16. Maz’ya V. G., On the behavior near the boundary of solutions to the Dirichlet problem for the biharmonic operator, Dokl. Akad. Nauk SSSR, 18 (1977), 15–19. English transl.: Soviet Math. Dokl. 18 (1977), 1152–1155 (1978). (1977) 
  17. Maz’ya V. G., Behavior of solutions to the Dirichlet problem for the biharmonic operator at a boundary point, In: Equadiff IV, Lecture Notes in Math. 703, Springer-Verlag, Berlin 1979, 250–262. (1979) 
  18. Maz’ya V. G. Donchev T., On the Wiener regularity of a boundary point for the polyharmonic operator, Dokl. Bolg. AN 36 (1983), 177–179; English transl.: Amer. Math. Soc. Transl. 137 (1987), 53–55. (1983) MR0709006
  19. Maz’ya V. G., Unsolved problems connected with the Wiener criterion, The Legacy of Norbert Wiener: A Centennial Symposium, Proc. Symp. Pure Math. vol. 60, American Mathematical Society, Providence, RI 1997, 199-208. (1997) Zbl0883.35050MR1460283
  20. Maz’ya V. G., On the regularity at the boundary of solutions to elliptic equations and conformal mappings, Dokl. Akad. Nauk SSSR 152 (1963), 1297–1300. English transl.: Soviet Math. Dokl. 4 (1963), 1547–1551. (1963) MR0163053
  21. Maz’ya V. G., Behavior near the boundary of solution to the Dirichlet problem for the second order elliptic operator in divergence form, Mat. Zametki 2 (1967), 209–220. (1967) MR0219873
  22. Maz’ya V. G., On the continuity modulus of a harmonic function at a boundary point, Zapiski Nauch. Sem. LOMI, Leningrad, Nauka, 135 (1981), 87–95. (1981) MR0741698
  23. Björn J., Maz’ya V. G., Capacitary estimates for solutions of the Dirichlet problem for second order elliptic equations in divergence form, Report LiTH-MAT-R-97-16, Linköping University. Zbl0961.35035
  24. Maz’ya V. G. Tashchiyan G. M., On the behavior of the gradient of a solution of the Dirichlet problem for the biharmonic equation near a boundary point of a three-dimensional domain, Sibirsk. Math. Zh. 31 (1990), 113–126. English transl.: Siberian Math. J. 31 (1991), 970–982. (1990) MR1097961
  25. Maz’ya V. G. Plamenevskii B. A., On the maximum principle for the biharmonic equation in a domain with conic points, Izv. Vyssh. Ucheb. Zaved. Mat. 2 (1981), 52–59. English transl.: Soviet Math. (Izv. VUZ) 25 (1981), 61–70. (1981) MR0614817
  26. Maz’ya V. G. Plamenevskii B. A., Properties of solutions to three-dimensional problems of elasticity theory and hydrodynamics in domains with isolated singular points, Dinamika sploshnoy sredy, Novosibirsk 50 (1981), 99–121. (1981) MR0639068
  27. Maz’ya V. G. Nasarow S. A., Plamenevskii B. A., Asymptotische Theorie elliptischer Randwertaufgaben in singulär gestörten Gebieten, 1, Akademie-Verlag, Berlin 1991. (1991) 
  28. Maz’ya V. G. Nazarov S. A., The vertex of a cone can be irregular in the Wiener sense for an elliptic equation of the fourth order, Mat. Zametki 39 (1986), 24–28. English transl.: Math. Notes 39 (1986), 14–16. (1986) MR0830840
  29. Kozlov V. A., Maz’ya V. G., Spectral properties of operator pencils generated by elliptic boundary value problems in a cone, Funktsional. Anal. i Prilozhen. 22 (1988), 38–46. English transl.: Functional Anal. Appl. 22 (1988), 114–121. (1988) MR0947604
  30. Landkof N. S., Foundations of modern potential theory, Springer-Verlag, Berlin 1972. (1972) Zbl0253.31001MR0350027
  31. Carathéodory C., Vorlesungen über reelle Funktionen, Leipzig and Berlin, 1918. (1918) 
  32. Vainberg M. M., Variational methods for the study of nonlinear operators, Holden-Day, San Francisco 1964. (1964) Zbl0122.35501MR0176364
  33. Eilertsen S., On weighted positivity of certain differential and pseudodifferential operators, Linköping Studies in Science and Technology. Theses No. 617, 1997. (1997) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.