# 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

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topAnna 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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- [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] E. Fabes and C. Kenig, On the space ${H}^{1}$ of a ${C}^{1}$-domain, Ark. Mat. 19 (1981), 1-22.
- [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] 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] C. Fefferman and E. Stein, ${H}^{p}$ spaces of several variables, Acta Math. 129 (1972), 137-193. Zbl0257.46078
- [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] A. Grimaldi, U. Neri and F. Ragnedda, Invertibility of some heat potentials in BMO-norms, ibid. 75 (1986), 77-90. Zbl0615.35007
- [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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