SCHAUDER ESTIMATES OF THE SOLUTION OF THE INVERSE PROBLEM
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This article investigates the Schauder estimates for solutions of inverse problems associated with partial differential equations. The study focuses on the regularity properties of the solutions and the dependence of these solutions on boundary and initial data. Using advanced functional analysis tools and the theory of Hölder spaces, new a priori estimates are established that guarantee the stability and smoothness of the reconstructed functions. The results provide a theoretical foundation for numerical algorithms applied to inverse problems in mathematical physics, such as heat conduction and diffusion processes.
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