Well-Posedness of SI Problem for an Elliptic Equation in a Banach Space with Mixed Boundary Conditions

In present study, we discuss the next source identification (SI) boundary value problem (BVP) for an elliptic equation $$-v^{\prime\prime}(t)+Av(t)=g(t)+p,\quad t\in(0,T),$$ $$v^{\prime}(0)=\varphi,\quad v^{\prime}(T)=\psi,\quad v(\gamma)=\zeta$$ in an arbitrary Banach space $$E$$ with a positive operator $$A$$ . The exact inequalities for SI problem in several Hölder norms are established. Afterward, coercive stability inequalities for three multidimensional elliptic BVPs are established in apps.

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