We establish a Lipschitz stability inequality for the problem of determining the nonlinear term in a quasilinear elliptic equation by boundary measurements. We give a proof based on a linearization procedure together with special solutions constructed from the fundamental solution of the linearized problem.
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Mourad Choulli 1
@article{CRMATH_2023__361_G9_1455_0, author = {Mourad Choulli}, title = {Stable determination of the nonlinear term in a quasilinear elliptic equation by boundary measurements}, journal = {Comptes Rendus. Math\'ematique}, pages = {1455--1470}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.484}, language = {en}, }
TY - JOUR AU - Mourad Choulli TI - Stable determination of the nonlinear term in a quasilinear elliptic equation by boundary measurements JO - Comptes Rendus. Mathématique PY - 2023 SP - 1455 EP - 1470 VL - 361 PB - Académie des sciences, Paris DO - 10.5802/crmath.484 LA - en ID - CRMATH_2023__361_G9_1455_0 ER -
Mourad Choulli. Stable determination of the nonlinear term in a quasilinear elliptic equation by boundary measurements. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1455-1470. doi : 10.5802/crmath.484. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.484/
[1] The Calderón inverse problem for isotropic quasilinear conductivities, Adv. Math., Volume 391 (2021), 107956 | Zbl
[2] An inverse problem for the Riemannian minimal surface equation, J. Differ. Equations, Volume 379 (2024), pp. 626-648 | DOI | MR
[3] Comments on the determination of the conductivity at the boundary from the Dirichlet-to-Neumann map, J. Math. Anal. Appl., Volume 517 (2023) no. 2, 126638, 31 pages | Zbl
[4] Hölder stability for a semilinear elliptic inverse problem, J. Math. Anal. Appl., Volume 530 (2024) no. 1, 127639 | DOI | Zbl
[5] Stability inequality for a semilinear elliptic inverse problem, NoDEA, Nonlinear Differ. Equ. Appl., Volume 28 (2021) no. 4, 37, 26 pages | Zbl
[6] Simultaneous identification of diffusion and absorption coefficients in a quasilinear elliptic problem, Inverse Probl., Volume 30 (2014) no. 3, 035009 | MR | Zbl
[7] On the uniqueness of nonlinear diffusion coefficients in the presence of lower order terms, Inverse Probl., Volume 33 (2017) no. 11, 115005 | MR | Zbl
[8] Elliptic partial differential equations of second order, Grundlehren der Mathematischen Wissenschaften, 224, Springer, 1983 | Zbl
[9] Unique determination of potentials and semilinear terms of semilinear elliptic equations from partial Cauchy data, J. Inverse Ill-Posed Probl., Volume 21 (2013), pp. 85-108 | DOI | MR | Zbl
[10] Global uniqueness for a semilinear elliptic inverse problem, Commun. Pure Appl. Math., Volume 47 (1994) no. 10, pp. 1403-1410 | DOI | MR | Zbl
[11] On E. E. Levi’s method of constructing a fundamental solution for second-order elliptic equations, Rend. Circ. Mat. Palermo, Volume 41 (1992) no. 2, pp. 251-294 | DOI | MR | Zbl
[12] Identification of nonlinearity in a conductivity equation via the Dirichlet-to-Neumann map, Inverse Probl., Volume 18 (2002) no. 4, pp. 1079-1088 | DOI | MR | Zbl
[13] Lipschitz and Hölder stable determination of nonlinear terms for elliptic equations (2022) | arXiv
[14] Partial data inverse problems for quasilinear conductivity equations (2020) (to appear in Mathematische Annalen) | arXiv
[15] Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities, Math. Res. Lett., Volume 27 (2020) no. 6, pp. 1801-1824 | DOI | MR | Zbl
[16] A remark on partial data inverse problems for semilinear elliptic equations, Proc. Am. Math. Soc., Volume 148 (2020) no. 2, pp. 681-685 | DOI | MR | Zbl
[17] Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations (2019) | arXiv
[18] Inverse problems for elliptic equations with power type nonlinearities, J. Math. Pures Appl., Volume 145 (2021), pp. 44-82 | DOI | MR | Zbl
[19] The Calderón problem for quasilinear elliptic equations, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, Volume 37 (2020) no. 5, pp. 1143-1166 | Zbl
[20] On a quasilinear inverse boundary value problem, Math. Z., Volume 221 (1996) no. 2, pp. 293-305 | MR | Zbl
[21] Inverse problems in quasilinear anisotropic media, Am. J. Math., Volume 119 (1997) no. 4, pp. 771-797 | MR | Zbl
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