Dirichlet problem for a linear elliptic equation in unbounded domains with $L^2$-boundary data

Chabrowski, J.

Dirichlet problem for a linear elliptic equation in unbounded domains with

L^{2}

-boundary data

Chabrowski, J.

Rendiconti del Seminario Matematico della Università di Padova, Tome 71 (1984), pp. 287-328.

MR Zbl | 1 citation dans Numdam

@article{RSMUP_1984__71__287_0,
     author = {Chabrowski, J.},
     title = {Dirichlet problem for a linear elliptic equation in unbounded domains with $L^2$-boundary data},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {287--328},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {71},
     year = {1984},
     mrnumber = {769444},
     zbl = {0557.35037},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_1984__71__287_0/}
}

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Chabrowski, J. Dirichlet problem for a linear elliptic equation in unbounded domains with $L^2$-boundary data. Rendiconti del Seminario Matematico della Università di Padova, Tome 71 (1984), pp. 287-328. http://www.numdam.org/item/RSMUP_1984__71__287_0/

Bibliographie
Cité par

[1] F. Acanfora, Problema esterno di Dirichlet per una classe di equazioni ellittiche del secondo ordine, Rend. Accad. Sei. Fis. Mat. Napoli, 65 (1979), pp. 59-69. | Zbl

[2] V. Benci - D. Fortunato, Second order elliptic operators on unbounded domains, Boll. Un. Mat. Ital., (5), 15 (1978), pp. 193-209. | MR | Zbl

[3] G. Bottaro - M.E. Marina, Problema di Dirichlet per equazioni ellittiche di tipo variazionale su insiemi non limitati, Boll. Un. Mat. Ital., (4), 8 (1973), pp. 46-56. | MR | Zbl

[4] J. Chabrowski - B. Thompson, On traces of solutions of a semi-linear partial differential equations of elliptic type, to appear in Ann. Polon. Math. | MR | Zbl

[5] J. Chabrowski - B. Thompson, On the boundary values of solutions of linear elliptic equations, Bull. Austral. Math. Soc., 27 (1983), pp. 1-30. | MR | Zbl

[6] J. Chabrowski, Note on nontangential boundary limits of solutions of elliptic equations in divergence form, to appear in Manuseripta Math.

[7] M. Chicco, An apriori inequality concerning elliptic, second order partial differential equations of variational type, Matematiche (Catania), 26 (1971), pp. 172-182. | MR | Zbl

[8] B.E.J. Dahlberg, On the Poisson integral for Lipschitz and C1-domains, Studia Math., 64 (1979), pp. 13-24. | MR | Zbl

[9] H. Federer - W.H. Fleming, Normal and integral currents, Ann. of Math., 72 (1960), pp. 458-520. | MR | Zbl

[10] D. Gilbarg - N.S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin - Heidelberg - New York, 1977. | MR | Zbl

[11] A.K. Guscin - V.P. Mikhailov, On the boundary values in L- (p > 1) of solutions of elliptic equations, Mat. Sb., 108 (150) (1979), pp. 1-19. | MR

[12] D.S. Jerison - C.E. Kenig, Boundary behaviour of harmonic functions in non-tangentially accessible domains, preprint, Department of Mathematics, Princeton University.

[13] D.S. Jerison - C.E. Kenig, Boundary value problems in Lipschitz domains, preprint.

[14] D.S. Jerison - C.E. Kenig, The Dirichlet problem in nonsmooth domains, Ann. of Math., 13 (1981), pp. 367-382. | MR | Zbl

[15] J.V. Kapanadze, On boundary values of a second order linear elliptic equations, Bulletin of the Academy of Science of the Georgian S.S.R., 93 (1979), pp. 285-288. | MR | Zbl

[16] O.A. Ladyzhenskaja - N.N. Ural'Tseva, Linear and quasilinear elliptic equations, Academic Press, New York and London, 1968. | MR | Zbl

[17] J. Lions - E. Magenes, Problèmes aux limites non homogenes et applications, vol. 1, Dunod, Paris, 1968. | MR | Zbl

[18] V.P. Mikhailov, Boundary values of solutions of elliptic equations in the ball, Mat. Sb., 100 (142) (1972), pp. 1-13.

[19] V.P. Mikhailov, Dirichlet's problem for a second order elliptic equation, Differential'nye Uravnenija, 12 (1976), pp. 1877-1891. | MR | Zbl

[20] V.P. Mikhailov, On the boundary values of the solutions of elliptic equations, Appl. Mat. Optim., 6 (1980), pp. 193-199. | MR | Zbl

[21] V.P. Mikhailov, Partial differential equations, Mir Publishers, Moscow, 1978. | MR | Zbl

[22] J. Ne, On the regularity of second order elliptic partial differential equations with unbounded Dirichlet integral, Arch. Rational Mech. Anal., 9 (1962), pp. 134-144. | MR | Zbl

[23] J. Necas, Les methodes directes en théorie des équations elliptiques, Academia, Éditeurs, Prague, 1967. | MR

[24] G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble), 15 (1969), pp. 189-258. | Numdam | MR | Zbl

[25] G. Stampacchia, Équations elliptiques du second ordre à coefficients discontinus, Les Presses de l'Université de Montréal, Séminaire de Mathétiques Supérieurs (1965). | MR | Zbl

[26] E. Stein, Singular integrals and differentiability properties of functions, Princeton University Press, Princeton, New Jersey, 1970. | MR | Zbl