A maximal regularity result with applications to parabolic problems with nonhomogeneous boundary conditions
Guidetti, Davide
Rendiconti del Seminario Matematico della Università di Padova, Tome 84 (1990), p. 1-37 / Harvested from Numdam
Publié le : 1990-01-01
@article{RSMUP_1990__84__1_0,
     author = {Guidetti, Davide},
     title = {A maximal regularity result with applications to parabolic problems with nonhomogeneous boundary conditions},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {84},
     year = {1990},
     pages = {1-37},
     mrnumber = {1101280},
     zbl = {0727.35065},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_1990__84__1_0}
}
Guidetti, Davide. A maximal regularity result with applications to parabolic problems with nonhomogeneous boundary conditions. Rendiconti del Seminario Matematico della Università di Padova, Tome 84 (1990) pp. 1-37. http://gdmltest.u-ga.fr/item/RSMUP_1990__84__1_0/

[ADN] S. Agmon - A. Douglis - L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math., 12 (1959), pp. 623-727. | MR 125307 | Zbl 0093.10401

[AG] S. Agmon, On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Comm. Pure Appl. Math., 15 (1962), pp. 119-147. | MR 147774 | Zbl 0109.32701

[AM] H. Amann, Quasilinear parabolic systems under nonlinear boundary conditions, Arch. Rat. Mech. Anal., 92 (2) (1986), pp. 153-192. | MR 816618 | Zbl 0596.35061

[AR] L. Arkeryd, On the Lp estimates for elliptic boundary problems, Math. Scand., 19 (1966), pp. 59-76. | MR 224970 | Zbl 0152.11202

[AT] P. Acquistapace - B. Terreni, On quasilinear parabolic systems, Math. Ann., 282 (1988), pp. 315-335. | MR 963019 | Zbl 0629.34018

[AV] M.S. Agranovic - M.I. Vishik, Elliptic problems with a parameter and parabolic problems of general type, Russian Math. Surveys, 19 (1964), pp. 53-157. | MR 192188 | Zbl 0137.29602

[BL] J. Bergh - J. Lofstrom, Interpolation spaces - An introduction, Springer Verlag (1976). | MR 482275 | Zbl 0344.46071

[BR1, 2, 3] F. Browder, A priori estimates for solutions of elliptic boundary value problems, Indag. Math. I, II 22 (1960), pp. 149-159, 160-169; III 23 (1961), pp. 404-410. | MR 147768 | Zbl 0096.30202

[DPG] G. Da Prato - P. Grisvard, Equations d'evolution abstraites non lineaires de type parabolique, Ann. Mat. Pura Appl., IV ser., 22 (1979), pp. 329-396. | MR 551075 | Zbl 0471.35036

[FR] A. Friedman, Partial differential equations of parabolic type, Prentice Hall Inc (1964). | MR 181836 | Zbl 0144.34903

[GM] M. Giaquinta - L. Modica, Local existence for quasilinear parabolic systems under nonlinear boundary conditions, Ann. Mat. Pura Appl., IV-149 (1987), pp. 41-60. | MR 932775 | Zbl 0655.35049

[GR] P. Grisvard, Spazi di tracce e applicazioni, Rend. Matem. Roma (VI) 5-II (1972), pp. 657-729. | MR 341059 | Zbl 0272.46025

[LU] A. Lunardi, Maximal space regularity in nonhomogeneous initial boundary value parabolic problems, preprint. | MR 989538 | Zbl 0653.35047

[SH] E. Shamir, Une propriété des espaces Hs,p, C. R. Acad. Sci. Paris, A-B 255 (1962), pp. 448-449. | MR 143015 | Zbl 0108.11001

[SO1] V.A. Solonnikov, Boundary value problems of mathematical physics. III (ed. O. A. O. A. Ladyzenskaya), Proc. Steklov Inst. Math., 83 (1965). | MR 211083

[SO2 A. Solonnikov, Estimates in Lp of solutions of elliptic and parabolic systems, in Boundary value problems of mathematical physics V (ed. O. A. Ladyzenskaya), Proc. Steklov Inst. Math., 102 (1967), pp. 157-185. | Zbl 0204.42101

[ST] E. Stein, Singular integrals and differentiability properties of functions, Princeton University Press (1970). | MR 290095 | Zbl 0207.13501

[TE 1] B. Terreni, Nonhomogeneous initial boundary value problems for linear parabolic systems, Studia Math., 42 (1989), pp. 141-175. | MR 986945 | Zbl 0703.35085

[TE2] B. Terreni, Hölder regularity results for non-homogeneous parabolic initial boundary value problems, preprint.

[TR] H. Triebel, On Besov-Hardy-Sobolev spaces in domains and regular elliptic boundary value problems : the case 0 < p < + ∞ Comm. P.D.E., 3 (12) (1978), pp. 1083-1164. | Zbl 0403.35034

[ZO] J.L. Zolesio, Multiplication dans les espaces de Besov, Proc. Royal Soc. Edimburgh, 78A (1977), pp. 113-117. | MR 500121 | Zbl 0382.46020