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 -