The Geometric Measure Theoretical Characterization of Viscosity Solutions to Parabolic Monge-Ampere Type Equation |
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Authors: | Wang Rouhuai Wang Guanglie |
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Abstract: | By an involved approach a geometric measure theory is established for parabolic Monge-Ampère operator acting on convex-monotone functions, the theory bears complete analogy with Aleksandrov's classical ones for elliptic Monge-Ampère operator acting on convex functions. The identity of solutions in weak and viscosity sense to parabolic Monge-Ampère equation is proved. A general result on existence and uniqueness of weak solution to BVP for this equation is also obtained. |
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Keywords: | geometric measure theory parabolic Monge-Ampère operator weak (or generalized) and viscosity solution |
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