Abstract:
We formulate a nonlocal boundary-value problem for a second order multidimensional equation of mixed type covering classical elliptic, hyperbolic, and parabolic equations. We prove regular solvability of the posed nonlocal boundary-value problem in Sobolev spaces.
Keywords:second order multidimensional equation of mixed type, nonlocal boundary value problem, generalized solution, regular solution, uniqueness, existence, smoothness of solution, method of $\varepsilon$-regularization, Galerkin method, a priori estimates.
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