SCHAUDER ESTIMATES OF THE SOLUTION OF THE INVERSE PROBLEM

Authors

  • Kurbanova Rukhsora Javliyevna

DOI:

https://doi.org/10.55640/

Keywords:

Schauder estimates; inverse problem; partial differential equations; Hölder spaces; regularity; stability; a priori estimates.

Abstract

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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References

1.Gilbarg D., Trudinger N.S. Elliptic Partial Differential Equations of Second Order. Berlin: Springer-Verlag, 2001.

2.Ladyzhenskaya O. A., Ural’tseva, N. N. Linear and Quasilinear Elliptic Equations. New York: Academic Press, 1968.

3.Morrey C.B. Multiple Integrals in the Calculus of Variations. Berlin: Springer, 1966.

4.Isakov V. Inverse Problems for Partial Differential Equations. New York: Springer, 2006.

5.Evans L.C. Partial Differential Equations. Providence: American Mathematical Society, 2010.

6.Agmon S. Douglas A.​ Nirenberg L. otsenka resheniy ellipticheskikh uravneniy vblizi granitsy .M : IL. 1962.-205 p.

7.Bers L. John F. Schechter M. Uravneniya s chastnymi proizvodnymi.M:. Mir. 1966.-351p.

8.Bitsadze A.., Kurant R.Uravnenie chastnymi proizvodnymi .Moskva 1964.

9.Ladyjenskaya.O.A, Uraltseva N.N Linear and quasi-linear equations of elliptical type. M : Nauka. 1973.-576p.

10. Hormander. lineynye differential'nye operatory s chastnymi proizvodnymi. M: Mir. 1965.-379p.

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Published

2025-10-29

Issue

Vol. 4 No. 9 (2025): Journal of Multidisciplinary Sciences and Innovations

Section

Articles

License

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This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors retain the copyright of their manuscripts, and all Open Access articles are disseminated under the terms of the Creative Commons Attribution License 4.0 (CC-BY), which licenses unrestricted use, distribution, and reproduction in any medium, provided that the original work is appropriately cited. The use of general descriptive names, trade names, trademarks, and so forth in this publication, even if not specifically identified, does not imply that these names are not protected by the relevant laws and regulations.

How to Cite

SCHAUDER ESTIMATES OF THE SOLUTION OF THE INVERSE PROBLEM. (2025). Journal of Multidisciplinary Sciences and Innovations, 4(9), 1413-1420. https://doi.org/10.55640/

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