Classical boundary value problems for integrable temperatures in a C 1 domain

Anna Grimaldi Piro; Francesco Ragnedda

Annales Polonici Mathematici (1991)

  • Volume: 54, Issue: 1, page 29-44
  • ISSN: 0066-2216

Abstract

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Abstract. We study a Neumann problem for the heat equation in a cylindrical domain with C 1 -base and data in h c 1 , a subspace of L 1. We derive our results, considering the action of an adjoint operator on B T M O C , a predual of h c 1 , and using known properties of this last space.

How to cite

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Anna Grimaldi Piro, and Francesco Ragnedda. "Classical boundary value problems for integrable temperatures in a $C^1$ domain." Annales Polonici Mathematici 54.1 (1991): 29-44. <http://eudml.org/doc/266112>.

@article{AnnaGrimaldiPiro1991,
abstract = {Abstract. We study a Neumann problem for the heat equation in a cylindrical domain with $C^1$-base and data in $h^1_c$, a subspace of $L^$1. We derive our results, considering the action of an adjoint operator on $B_TMOC$, a predual of $h^1_c$, and using known properties of this last space.},
author = {Anna Grimaldi Piro, Francesco Ragnedda},
journal = {Annales Polonici Mathematici},
keywords = {Neumann problem; nontangential limit; single layer potential},
language = {eng},
number = {1},
pages = {29-44},
title = {Classical boundary value problems for integrable temperatures in a $C^1$ domain},
url = {http://eudml.org/doc/266112},
volume = {54},
year = {1991},
}

TY - JOUR
AU - Anna Grimaldi Piro
AU - Francesco Ragnedda
TI - Classical boundary value problems for integrable temperatures in a $C^1$ domain
JO - Annales Polonici Mathematici
PY - 1991
VL - 54
IS - 1
SP - 29
EP - 44
AB - Abstract. We study a Neumann problem for the heat equation in a cylindrical domain with $C^1$-base and data in $h^1_c$, a subspace of $L^$1. We derive our results, considering the action of an adjoint operator on $B_TMOC$, a predual of $h^1_c$, and using known properties of this last space.
LA - eng
KW - Neumann problem; nontangential limit; single layer potential
UR - http://eudml.org/doc/266112
ER -

References

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  1. [1] R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. Zbl0358.30023
  2. [2] E. Fabes, M, Jodeit and N. Rivière, Potential techniques for boundary value problems on C l -domain, Acta Math. 141 (1978), 165-186. Zbl0402.31009
  3. [3] E. Fabes and C. Kenig, On the space H 1 of a C 1 -domain, Ark. Mat. 19 (1981), 1-22. 
  4. [4] E. Fabes, C. Kenig and U. Neri, Carleson measures, H l duality anti weighted BMO in non-smooth domains, Indiana Univ. Math. J. 30 (1981), 574-581. Zbl0441.31004
  5. [5] E. Fabes and N. Rivière, Dirichlet and Neumann problems for the heat equation on C'-cylinder, in: Proc. Sympos. Pure Math. 35, Part 2, Amer. Math. Soc., 1979, 179-196. Zbl0436.35039
  6. [6] C. Fefferman and E. Stein, H p spaces of several variables, Acta Math. 129 (1972), 137-193. Zbl0257.46078
  7. [7] A. Grimaldi, U. Neri and F. Ragnedda, BMO continuity for some heat potentials, Rend. Sem. Mat. Univ. Padova 72 (1984), 289-305. Zbl0561.35037
  8. [8] A. Grimaldi, U. Neri and F. Ragnedda, Invertibility of some heat potentials in BMO-norms, ibid. 75 (1986), 77-90. Zbl0615.35007
  9. [9] A. Grimaldi and F. Ragnedda, Properties and geometrical structure of the boundary of a C 1 -cylindrical domain, Rend. Sem. Mat. Univ. Cagliari, to appear. Zbl0555.35059

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