Far East Journal of Applied Mathematics

The Far East Journal of Applied Mathematics publishes original research papers and survey articles in applied mathematics, covering topics such as nonlinear dynamics, approximation theory, and mathematical modeling. It encourages papers focusing on algorithm development.

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REDUCTION OF MONOTONE OPERATORS TO LINEAR EQUATIONS

Authors

  • N. A. D’Auria

DOI:

https://doi.org/10.17654/0972096022011

Abstract

We establish some regularity results for local solutions of equations associated to a class of monotone operators (also multivalued), reducing our problems to linear equations.

Received: May 2, 2022
Accepted: June 7, 2022

References

C. Capone, Quasiharmonic fields and Beltrami operators, Comment. Math. Univ. Carolin. 43 (2002), 363-377.

V. Chiadò Piat, G. Dal Maso and A. De Franceschi, G-convergence of monotone operators, Ann. Inst. H. Poincaré C Anal. Non Linèaire 7(3) (1990), 123-160.

E. De Giorgi, Sulla differenziabilità e l’analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Nat. (3) 3 (1957), 25-43 (in Italian).

E. Giusti, Metodi diretti nel calcolo delle variazioni, Unione Matematica Italiana, Bologna, 1994 (in Italian).

T. Iwaniec and C. Sbordone, Quasiharmonic fields, Ann. Inst. H. Poincaré C Anal. Non Linèaire) 18(5) (2001), 519-572.

F. Leonetti and V. Nesi, Quasiconformal solutions to certain first order systems and the proof of a conjecture of G. W. Milton, J. Math. Pures Appl. (9) 76(2) (1997), 109-124.

N. Meyers, An -estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scoula Norm. Sup. Pisa Cl. Sci. (3) 17 (1963), 189-206.

L. Piccinini and S. Spagnolo, On the Hölder continuity of solutions of second order elliptic equations in two variables, Ann. Scoula Norm. Sup. Pisa Cl. Sci. (3) 26 (1972), 391-402.

R. T. Rockafellar, Convex analysis, Princeton Mathematical Series, Princeton University Press, Princeton , N.J., 1970.

M. Ruzhansky, H. Dutta and R. P. Agarwal, Mathematical Analysis and Applications: Selected Topics, John Wiley & Sons, 2018.

C. Sbordone, Reduction of nonlinear PDEs to linear equations, Milan J. Math. 71 (2003), 19-32.

S. Spagnolo, Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche, Ann. Scoula Norm. Sup. Pisa Cl. Sci. (3) 22 (1968), 571-597 (in Italian).

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Published

2022-06-17

Issue

Vol. 113 (2022)

Section

Articles

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How to Cite

REDUCTION OF MONOTONE OPERATORS TO LINEAR EQUATIONS. (2022). Far East Journal of Applied Mathematics, 113, 67-79. https://doi.org/10.17654/0972096022011