Optimal Three Cylinder Inequality at the Boundary for Solutions to Parabolic Equations and Unique Continuation Properties
SergioVESSELLA · Acta Scientiarum Naturalium Universitatis Sunyatseni · 2005
Let Γ be a portion of a C^1,α boundary of an n-dimensional domain D. Let u be a solution to a second order parabolic equation in D×(-T,T) and assume that u = 0 on Γ×(-T,T), 0∈Γ. We prove that u satisfies a three cylinder inequality near Γ (-T, T). As a consequence of the previous result we prove that if u （ix, t) = 0（|x|^k) for every t∈(-T,T) and every k∈N, then u is identically equal to zero.