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

• Autorzy: Anna Grimaldi Piro , Francesco Ragnedda
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35K05: Heat equation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991
• Tom: 54
• Numer: 1
• Strony: 29-44

Daty

wydano

1991

otrzymano

1989-12-02

Twórcy

autor

Anna Grimaldi Piro

• Dipartimento di Matematica, Università di Cagliari, Viale Merello 92, 09100 Cagliari, Italia

autor

Francesco Ragnedda

• Cagliari
• Dipartimento di Matematica, Università di Cagliari, Viale Merello 92, 09100 Cagliari, Italia

Bibliografia

• [1] R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645.
• [2] E. Fabes, M, Jodeit and N. Rivière, Potential techniques for boundary value problems on $C^l$-domain, Acta Math. 141 (1978), 165-186.
• [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.
• [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.
• [6] C. Fefferman and E. Stein, $H^p$ spaces of several variables, Acta Math. 129 (1972), 137-193.
• [7] A. Grimaldi, U. Neri and F. Ragnedda, BMO continuity for some heat potentials, Rend. Sem. Mat. Univ. Padova 72 (1984), 289-305.
• [8] A. Grimaldi, U. Neri and F. Ragnedda, Invertibility of some heat potentials in BMO-norms, ibid. 75 (1986), 77-90.
• [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.