Abstract
Abstract. The paper studies a second-order elliptic equation given on an infinite strip of width 2 and having variable intermediate and junior coefficients. We assume that the intermediate coefficients may not obey the potential. The problem is posed of finding a strong generalized solution of the equation that satisfies periodic conditions at the edges of the strip. The coefficients of the equation are smooth and not bounded functions. In terms of the coefficients themselves, the sufficient conditions for the existence and uniqueness of a solution to the problem posed are indicated, and a maximal regularity estimate for the solution is given. Their main difference from known results is the requirement of a different order of growth of intermediate coefficients for partial derivatives of an unknown function with respect to different variables. We also cover the case where the intermediate coefficients can grow at infinity faster than a linear function.
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