Article
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
References:
[1] Acquistapace, P.: On BMO regularity for linear elliptic system. Ann. Mat. Pura Appl. 161 (1992), 231–269. MR 1174819
[2] Agmon, S., Douglis, A., Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I. Comm. Pure Appl. Math. 12 (1959), 623–727. MR 0125307 | Zbl 0093.10401
[3] Agmon, S., Douglis, A., Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II. Comm. Pure Appl. Math. 17 (1964), 35–72. MR 0162050 | Zbl 0123.28706
[4] Bramanti, M., Cerutti, M.C.: $W^{1,2}_p$ solvability for the Cauchy-Dirichlet problem for parabolic equations with VMO coefficients. Comm. Partial Differential Equations 18 (1993), 1735–1763. MR 1239929 | Zbl 0816.35045
[5] Bureau, F.: Divergent integrals and partial differential equations. Comm. Pure Appl. Math. 8 (1955), 143–202. MR 0068085 | Zbl 0064.09204
[6] Calderón, A.P.: Integrales singulares y sus aplicaciones aecuaciones diferenciales hyperbolicas. Cursos y seminarios de Matematicas, 3, Univ. de Buenos Aires, 1960. MR 0123834
[7] Calderón, A.P.: Commutators of singular integral operators. Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1092–1099. MR 0177312
[8] Calderón, A.P.: Singular integrals. Bull. Amer. Math. Soc. 72 (1966), 427–465. MR 0209918
[9] Calderón, A.P., Zygmund, A.: On the existence of certain singular integrals. Acta Math. 88 (1952), 85–139. MR 0052553
[10] Calderón, A.P., Zygmund, A.: Singular integral operators and differential equations. Amer. J. Math. 79 (1957), 901–921. MR 0100768
[11] Calderón, A.P., Zygmund, A.: On singular integrals with variable kernels. Applicable Analysis 7 (1978), 221–238. MR 0511145
[12] Campanato, S.: Proprietà di hölderianità di alcune classi difunzioni. Ann. Scuola Norm. Sup. Pisa 17 (1963), 175–188. MR 0156188
[13] Campanato, S.: Equazioni ellittiche del secondo ordine e spazi L $^{2,\lambda }$. Ann. Mat. Pura Appl. 69 (1965), 321–382. MR 0192168
[14] Campanato, S.: Un risultato relativo ad equazioni ellittiche del secondo ordine di tipo non variazionale. Ann. Scuola Norm. Sup. Pisa 21 (1967), 701–707. MR 0224996 | Zbl 0157.42202
[15] Campanato, S.: Sistemi ellittici in forma divergenza. Regolarità all’interno. Quaderni Scuola Normale Superiore Pisa, 1980. MR 0668196 | Zbl 0453.35026
[16] Campanato, S.: Sistemi ellittici lineari e non lineari. Quaderno S.I.S.S.A., a.a. 1985–86.
[16$^{\prime }$] Campanato, S.: Su un teorema di interpolazione di G.Stampacchia. Ann. Scuola Norm. Sup. Pisa 20 (1966), 649–652. MR 0209864 | Zbl 0195.41102
[17] Campanato, S., Stampacchia, G.: Sulle maggiorazioni in $L^p$ nella teoria delle equazioni ellittiche. Boll. Un. Mat. Ital. 20 (1965), 393–399. MR 0192169
[18] Chiarenza, F., Frasca, M., Longo, P.: Interior $W^{2,p}$ estimates for non divergence elliptic equations with discontinuous coefficients. Ricerche Mat. 40 (1991), 149–168. MR 1191890
[19] Chiarenza, F., Frasca, M., Longo, P.: $W^{2,p}$-solvability of the Dirichlet problem for non divergence elliptic equations with VMO coefficients. Trans. Amer. Math. Soc. 336 (1993), 841–853. MR 1088476 | Zbl 0818.35023
[20] Chiarenza, F., Franciosi, M., Frasca, M.: $L^p$ estimates for linear elliptic systems with discontinuous coefficients. Rend. Acc. Lincei (9) 5 (1994), 27–32. MR 1273890
[21] Chicco, M.: Solvability of the Dirichlet problem in $H^{2,p} (\Omega )$ for a class of linear second order elliptic partial differential equations. Boll. Un. Mat. Ital. (4) 4 (1971), 374–387. MR 0298209
[22] Coifman, R., Rochberg, R., Weiss, G.: Factorization theorems for Hardy spaces in several variables. Ann. of Math. 103 (1976), 611–635. MR 0412721 | Zbl 0326.32011
[23] Coifman, R., Lions, P.L., Meyer, Y., Semmes, S.: Compensated compactness and Hardy spaces. J. Math. Pures Appl. 72 (1993), 247–286. MR 1225511 | Zbl 0864.42009
[24] Fazio, G. Di: $L^p$ estimates for divergence form elliptic equations with discontinuous coefficients. preprint. Zbl 1007.65053
[25] Fazio, G. Di: $L^p$ estimates for divergence form elliptic systems with discontinuous coefficients. preprint. Zbl 1007.65053
[26] Fazio, G. Di, Ragusa, M.A.: Interior estimates in Morrey spaces for strong solutions to non divergence form equations with discontinuous coefficients. J.Funct. Anal. 112 (1993), 241–256. MR 1213138
[27] Douglis, A., Nirenberg, L.: Interior estimates for elliptic system of partial differential equations. Comm. Pure Appl. Math. 8 (1955), 503–538. MR 0075417
[28] Fabes, E.: Singular integrals and partial differential equations of parabolic type. Studia Math. 28 (1966), 81–131. MR 0213744 | Zbl 0144.35002
[29] Fabes, E., Rivière, N.: Singular integrals with mixed homogeneity. Studia Math. 27 (1966), 19–38. MR 0209787
[30] Fefferman, C., Stein, E.: $H^p$ spaces of several variables. Acta Math. 129 (1972), 137–193. MR 0447953
[31] Giaquinta, M.: Multiple integrals in the calculus of variations and nonlinear elliptic system. Ann. of Math. Stud. 105 (1983), Princeton Univ. Press. MR 0717034
[32] Gilbarg, D., Trudinger, N.: Elliptic partial differential equations of second order. $2^{\text{nd}}$ edition, Springer-Verlag, 1983. MR 0737190 | Zbl 0562.35001
[33] Greco, D.: Nuove formule integrali di tipo ellittico ed applicazioni alla teoria del potenziale. Ricerche Mat. 5 (1956), 126–149. MR 0082030
[34] Hardy, G., Littlewood, J., Polya, G.: Inequalities. Cambridge Univ. Press, 1952. MR 0046395 | Zbl 0047.05302
[35] Hellwig, G.: Partial Differential Equations. Blaisdell Publishing Co., 1964. Zbl 0133.35701
[36] Janson, S.: On functions with conditions on the mean oscillation. Ark. Mat. 14 (1976), 189–196. MR 0438030 | Zbl 0341.43005
[37] Janson, S.: Mean oscillation and commutators of singular integrals operators. Ark. Mat. 16 (1978), 263–270. MR 0524754
[38] John, F.: The fundamental solution of linear elliptic differential equations with analytic coefficients. Comm. Pure Appl. Math. 3 (1950), 273–304. MR 0042030 | Zbl 0041.06203
[39] John, F., Nirenberg, L.: On functions of bounded mean oscillation. Comm. Pure Appl. Math. 14 (1961), 415–426. MR 0131498 | Zbl 0102.04302
[40] Koshelev, A.I.: On boundedness in $L^p$ of solutions of elliptic differential equations. Mat. Sb. 38 (1956), 359–372. MR 0078563
[41] Meyers, N.: An $L^p$ estimate for the gradient of solutions of second order elliptic divergence equations. Ann. Scuola Norm. Sup. Pisa 17 (1963), 189–206. MR 0159110
[42] Meyers, N.: Mean oscillation over cubes and Hölder continuity. Proc. Amer. Math. Soc. 15 (1964), 717–721. MR 0168712 | Zbl 0129.04002
[43] Miranda, C.: Partial differential equations of elliptic type. $2^{\text{nd}}$ ed., Springer-Verlag, 1970. MR 0284700 | Zbl 0198.14101
[44] Morrey, C.B.: Multiple integrals in the calculus of variations. Springer-Verlag, 1966. MR 0202511 | Zbl 0142.38701
[45] Neri, U.: Singular integrals. Lect. Notes Mathematics, 200, Springer Verlag, 1971. MR 0463818 | Zbl 0219.44006
[46] Neri, U.: Fractional integration on the space $H^1$ and its dual. Studia Math. 53 (1975), 175–189. MR 0388074
[47] Neri, U.: Some properties of bounded mean oscillation. Studia Math. 41 (1977), 63–75. MR 0445210
[48] Palagachev, D.K.: Quasilinear elliptic equations with $\text{\rm {VMO}}$ coefficients. preprint. MR 1308019
[49] Sarason, D.: Functions of vanishing mean oscillation. Trans. Amer.Math. Soc. 207 (1975), 391–405. MR 0377518 | Zbl 0319.42006
[50] Simader, C.: On Dirichlet’s boundary value problem. Lect. Notes Mathematics, 268, Springer-Verlag, 1972. MR 0473503 | Zbl 0242.35027
[51] Solonnikov, V.A.: On Green’s matrices for elliptic boundary value problems I. Proc. Steklov Inst. Math. 110 (1970), 123–170. MR 0289935
[52] Spanne, S.: Some function spaces defined using the mean oscillation over cubes. Ann. Scuola Norm. Sup. Pisa 19 (1965), 593–608. MR 0190729 | Zbl 0199.44303
[53] Stampacchia, G.: $\mathscr{L}^{p,\lambda}$ spaces and interpolation. Comm. Pure Appl. Math. 17 (1964), 293–306. MR 0178350
[53$^{\prime }$] Stampacchia, G.: The spaces $\mathscr{L}^{p,\lambda}$, $\mathscr{N}^{p,\lambda}$ and interpolation. Ann. Scuola Norm. Sup. Pisa 19 (1965), 443–462. MR 0199697
[54] Stein, E.: Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals. Princeton Univ. Press, 1993. MR 1232192 | Zbl 0821.42001
[55] Uchiyama, A.: On the compactness of operators of Hankel type. Tôhoku Math. J. 30 (1978), 163–171. MR 0467384 | Zbl 0384.47023
[56] Vitanza, C.: $W^{2,p}$ regularity for a class of elliptic second order equations with discontinuous coefficients. Matematiche 47 (1992), 177–186. MR 1229461
[57] Vitanza, C.: A new contribution to the $W^{2,p}$ regularity for a class of elliptic second order equations with discontinuous coefficients. to appear in Matematiche. MR 1320669
Search
Partner of
