Geodesic
Elliptic equations in convex domains
Algebra i analiz, Tome 29 (2017) no. 1, pp. 209-221.

Voir la notice de l'article provenant de la source Math-Net.Ru

A short survey of a series of results by the author, partly obtained in collaboration with Yu. Burago.
Keywords: harmonic function, double layer potential, Poisson equation, Sobolev space. 
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V. Maz'ya. Elliptic equations in convex domains. Algebra i analiz, Tome 29 (2017) no. 1, pp. 209-221. http://geodesic.mathdoc.fr/item/AA_2017_29_1_a8/

[1] Alkhutov Yu. A., Mazya V. G., “$L^{1,p}$-koertsitivnost i otsenki funktsii Grina zadachi Neimana v vypukloi oblasti”, Probl. mat. anal., 73, 2013, 3–16

[2] Burago Yu. D., Mazya V. G., Sapozhnikova V. D., “O potentsiale dvoinogo sloya dlya neregulyarnykh oblastei”, Dokl. AN SSSR, 147:3 (1962), 523–525 | Zbl

[3] Burago Yu. D., Mazya V. G., “Nekotorye voprosy teorii potentsiala i teorii funktsii dlya oblastei s neregulyarnymi granitsami”, Zap. nauch. semin. POMI, 3, 1967, 3–152 | MR | Zbl

[4] Cianchi A., Maz'ya V. G., “Global boundedness of the gradient for a class of nonlinear elliptic systems”, Arch. Ration. Mech. Anal., 212:1 (2014), 129–177 | DOI | MR | Zbl

[5] Cianchi A., Maz'ya V. G., “Gradient regularity via rearrangements for $p$-Laplacian type elliptic boundary value problems”, J. Eur. Math. Soc., 16:3 (2014), 571–595 | DOI | MR | Zbl

[6] Mayboroda S., Maz'ya V., “Boundedness of the Hessian of a biharmonic function in a convex domain”, Comm. Partial Differential Equation, 33:8 (2008), 1439–1454 | DOI | MR | Zbl

[7] Maz'ya V., “Boundary integral equations”, Analysis, v. IV, Encyclopaedia Math. Sci., 27, Springer, Berlin, 1991, 127–222 | DOI | MR

[8] Maz'ya V., Sobolev spaces with applications to elliptic partial differential equations, Grundlehren Math. Wiss., 342, 2nd ed., Springer, Heidelberg, 2011 | DOI | MR | Zbl