Solvability and maximal regularity results for a differential equation with diffusion coefficient

Authors: KORDAN OSPANOV, ADILET YESBAYEV

Abstract: We consider a second-order differential equation with rapidly growing intermediate coefficients. We obtain a solvability result in the cases that the diffusion coefficient of equation is unbounded or it tends to zero at the infinity. Under additional conditions, we prove the $L_p - $ maximal regularity estimate for the solution of this equation.

Keywords: Second-order differential equation, unbounded intermediate coefficient, existence of a solution, uniqueness, maximal regularity estimate

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