Existence and representation of solutions of parabolic equations
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- by Neil A. Eklund PDF
- Proc. Amer. Math. Soc. 47 (1975), 137-142 Request permission
Abstract:
Let $L$ be a linear, second order parabolic operator in divergence form and let $Q$ be a bounded cylindrical domain in ${E^{n + 1}}$. Let ${\partial _p}Q$ denote the parabolic boundary of $Q$. To each continuous function $f$ on ${\partial _p}Q$ there is a unique solution $u$ of the boundary value problem $Lu = 0$ in $Q,u = f$ on ${\partial _p}Q$. Moreover, for the given $L$ and $Q$, to each $(x,t) \in Q$ there is a unique nonnegative measure ${\mu _{(x,t)}}$ with support on ${\partial _p}Q$ such that the solution of the boundary value problem is given by $u(x,t) = \int _{{\partial _p}Q} {fd{\mu _{(x,t)}}}$.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 137-142
- MSC: Primary 35K20
- DOI: https://doi.org/10.1090/S0002-9939-1975-0361442-1
- MathSciNet review: 0361442