Second order unbounded parabolic equations in separated form

Tom 115 / 1995

Maciej Kocan Studia Mathematica 115 (1995), 291-310 DOI: 10.4064/sm-115-3-291-310


We prove existence and uniqueness of viscosity solutions of Cauchy problems for fully nonlinear unbounded second order Hamilton-Jacobi-Bellman-Isaacs equations defined on the product of two infinite-dimensional Hilbert spaces H'× H'', where H'' is separable. The equations have a special "separated" form in the sense that the terms involving second derivatives are everywhere defined, continuous and depend only on derivatives with respect to x'' ∈ H'', while the unbounded terms are of first order and depend only on derivatives with respect to x' ∈ H'.


  • Maciej Kocan

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