TY - JOUR

T1 - Weak solutions of parabolic equations in non-cylindrical domains

AU - Brown, Russell M.

AU - Hu, Wei

AU - Lieberman, Gary M.

PY - 1997

Y1 - 1997

N2 - In their classical work, Ladyzhenskaya and Ural'tseva gave a definition of weak solution for parabolic equations in cylindrical domains. Their definition was broad enough to guarantee the solvability of all such problems but narrow enough to guarantee the uniqueness of these solutions. We give here some alternative definitions which are appropriate to non-cylindrical domains, and we prove the unique solvability of such problems.

AB - In their classical work, Ladyzhenskaya and Ural'tseva gave a definition of weak solution for parabolic equations in cylindrical domains. Their definition was broad enough to guarantee the solvability of all such problems but narrow enough to guarantee the uniqueness of these solutions. We give here some alternative definitions which are appropriate to non-cylindrical domains, and we prove the unique solvability of such problems.

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U2 - 10.1090/s0002-9939-97-03759-3

DO - 10.1090/s0002-9939-97-03759-3

M3 - Article

AN - SCOPUS:21744436909

SN - 0002-9939

VL - 125

SP - 1785

EP - 1792

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 6

ER -