A maximal regularity result with applications to parabolic problems with nonhomogeneous boundary conditions

Davide Guidetti

Rendiconti del Seminario Matematico della Università di Padova (1990)

  • Volume: 84, page 1-37
  • ISSN: 0041-8994

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Guidetti, Davide. "A maximal regularity result with applications to parabolic problems with nonhomogeneous boundary conditions." Rendiconti del Seminario Matematico della Università di Padova 84 (1990): 1-37. <http://eudml.org/doc/108196>.

@article{Guidetti1990,
author = {Guidetti, Davide},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {maximal regularity; local existence},
language = {eng},
pages = {1-37},
publisher = {Seminario Matematico of the University of Padua},
title = {A maximal regularity result with applications to parabolic problems with nonhomogeneous boundary conditions},
url = {http://eudml.org/doc/108196},
volume = {84},
year = {1990},
}

TY - JOUR
AU - Guidetti, Davide
TI - A maximal regularity result with applications to parabolic problems with nonhomogeneous boundary conditions
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1990
PB - Seminario Matematico of the University of Padua
VL - 84
SP - 1
EP - 37
LA - eng
KW - maximal regularity; local existence
UR - http://eudml.org/doc/108196
ER -

References

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  1. [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. Zbl0093.10401MR125307
  2. [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. Zbl0109.32701MR147774
  3. [AM] H. Amann, Quasilinear parabolic systems under nonlinear boundary conditions, Arch. Rat. Mech. Anal., 92 (2) (1986), pp. 153-192. Zbl0596.35061MR816618
  4. [AR] L. Arkeryd, On the Lp estimates for elliptic boundary problems, Math. Scand., 19 (1966), pp. 59-76. Zbl0152.11202MR224970
  5. [AT] P. Acquistapace - B. Terreni, On quasilinear parabolic systems, Math. Ann., 282 (1988), pp. 315-335. Zbl0629.34018MR963019
  6. [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. Zbl0137.29602MR192188
  7. [BL] J. Bergh - J. Lofstrom, Interpolation spaces - An introduction, Springer Verlag (1976). Zbl0344.46071MR482275
  8. [BR1, 2, 3] F. Browder, A priori estimates for solutions of elliptic boundary value problems, Indag. Math. I, II22 (1960), pp. 149-159, 160-169; III23 (1961), pp. 404-410. Zbl0096.30202MR147768
  9. [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. Zbl0471.35036MR551075
  10. [FR] A. Friedman, Partial differential equations of parabolic type, Prentice Hall Inc (1964). Zbl0144.34903MR181836
  11. [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. Zbl0655.35049MR932775
  12. [GR] P. Grisvard, Spazi di tracce e applicazioni, Rend. Matem. Roma (VI) 5-II (1972), pp. 657-729. Zbl0272.46025MR341059
  13. [LU] A. Lunardi, Maximal space regularity in nonhomogeneous initial boundary value parabolic problems, preprint. Zbl0653.35047MR989538
  14. [SH] E. Shamir, Une propriété des espaces Hs, p, C. R. Acad. Sci. Paris, A-B255 (1962), pp. 448-449. Zbl0108.11001MR143015
  15. [SO1] V.A. Solonnikov, Boundary value problems of mathematical physics. III (ed. O. A. O. A. Ladyzenskaya), Proc. Steklov Inst. Math., 83 (1965). MR211083
  16. [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. Zbl0204.42101
  17. [ST] E. Stein, Singular integrals and differentiability properties of functions, Princeton University Press (1970). Zbl0207.13501MR290095
  18. [TE 1] B. Terreni, Nonhomogeneous initial boundary value problems for linear parabolic systems, Studia Math., 42 (1989), pp. 141-175. Zbl0703.35085MR986945
  19. [TE2] B. Terreni, Hölder regularity results for non-homogeneous parabolic initial boundary value problems, preprint. 
  20. [TR] H. Triebel, On Besov-Hardy-Sobolev spaces in domains and regular elliptic boundary value problems : the case 0 &lt; p &lt; + ∞ Comm. P.D.E., 3 (12) (1978), pp. 1083-1164. Zbl0403.35034
  21. [ZO] J.L. Zolesio, Multiplication dans les espaces de Besov, Proc. Royal Soc. Edimburgh, 78A (1977), pp. 113-117. Zbl0382.46020MR500121

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