The authors show the uniqueness of the ``good solution'' to the Cauchy-Dirichlet problem for linear non-variational parabolic equations with the coefficients of the principal part with discontinuities, in cases in which in general uniqueness of strong solutions in Sobolev spaces does not hold. The notion of the ``good solution'' to the elliptic equations was introduced by the first author in [M. C. Cerutti, L. Escauriaza and E. B. Fabes, Ann. Mat. Pura Appl. (4) 163 (1993), 161--180
Uniqueness for second-order parabolic equations with discontinuous coefficients
CERUTTI, MARIA CRISTINA;
2007-01-01
Abstract
The authors show the uniqueness of the ``good solution'' to the Cauchy-Dirichlet problem for linear non-variational parabolic equations with the coefficients of the principal part with discontinuities, in cases in which in general uniqueness of strong solutions in Sobolev spaces does not hold. The notion of the ``good solution'' to the elliptic equations was introduced by the first author in [M. C. Cerutti, L. Escauriaza and E. B. Fabes, Ann. Mat. Pura Appl. (4) 163 (1993), 161--180File in questo prodotto:
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