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We study some properties of the coincidence set for the boundary Signorini problem, improving some results from previous works by the second author and collaborators. Among other new results, we show here that the convexity assumption on the domain made previously in the literature on the location of the coincidence set can be avoided under suitable alternative conditions on the data.
Czasopismo
Rocznik
Tom
Strony
145--157
Opis fizyczny
Bibliogr. 25 poz,
Twórcy
autor
- University of Augsburg Department of Mathematics 86159 Augsburg, Germany
autor
- Universidad Complutense de Madrid Instituto de Matematica Interdisciplinar Plaza de Ciencias 3, 28040 Madrid, Spain
Bibliografia
- [1] M. de Benito Delgado, Sobre Un Problema de Contacto En Elasticidad, Bachelor's Thesis, Universidad Complutense de Madrid, Madrid, 2012.
- [2] H. Brezis, Proble.rn.es unilateraux, Journal de Mathematiques Pures et Appliquees 51 (1972), 1-168.
- [3] L. Caffarelli, L. Silvestre, An Extension problem related to the fractional Laplacian, Comm. Partial Differential Equations 32 (2007) 8, 1245-1260.
- [4] L.A. CafFarelli, Further regularity for the Signorini problem, Comm. Partial Differential Equations 4 (1979) 9, 1067-1075.
- [5] J. Davila, M. Montenegro, Nonlinear problems with solutions exhibiting a free boundary on the boundary, Ann. Inst. H. Poincare Anal. Non Lineaire 22 (2005) 3, 303-330.
- [6] M. Delfour, J. Zolesio, Shapes and Geometries, Advances in Design and Control, Society for Industrial and Applied Mathematics, 2011.
- [7] J. Diaz, Special Finite Time Extinction, Nonlinear Evolution Systems: Dynamic Boundary Conditions and Coulomb Friction Type Problems, [in:] H. Brezis, M. Chipot, J. Escher (eds), Nonlinear Elliptic and Parabolic Problems: A Special Tribute to the Work of Herbert Arnann, Birkhauser Basel, Progress in Nonlinear Differential Equations and Their Applications, 71-97, 2005.
- [8] J.I. Diaz, Localización de fronteras libres en inecuaciones variacionales estacionarias dadas por obstdculos, 3. Congreso de ecuaciones diferenciales y Aplicaciones, Universidad de Santander y Universidad Complutense de Madrid, Santiago, 1980, 1-12.
- [9] J.I. Diaz, R.F. Jimenez, Aplicación de la teoria no lineal de semigrupos a un operador pseudodiferencial, in Adas del VII GEDYA, SEMA, Granada, 1985, 137-142.
- [10] J.I. Diaz, R.F. Jimenez, Behaviour on the boundary of solutions of parabolic equations with nonlinear boundary condition: The evolutionary Signorini problem,, [in:] Andlisis No Lineal, PNUD/UNESCO, Univ. de Conception, 69-80, 1986.
- [11] J.I. Diaz, R.F. Jimenez, Boundary behaviour of solutions of the Signorini problem, Bolletino U.M.I 7 (1988) 2-B, 127-139.
- [12] J.I. Diaz, T. Mingazzini, Free boundaries touching the boundary of the domain for some reaction-diffusion problems, Nonlinear Anal. 119 (2015), 275-294.
- [13] J.I. Diaz, D. Gómez-Castro, A.V. Podolskiy, T.A. Shaposhnikova, Homogenization of a net of periodic critically scaled boundary obstacles related to reverse osmosis "nano-composite" membranes, Advances in Nonlinear Analysis (2018), https://doi.org/10.1515/anona-2018-0158.
- [14] J.I. Diaz, D. Gómez-Castro, J.L. Vazquez, The fractional Schrodinger equation with general nonnegative potentials. The weighted space approach, Nonlinear Anal. 177 (2018), 325-360.
- [15] G. Duvaut, J.L. Lions, Inequalities in Mechanics and Physics, vol. 219, Grundlehren der mathematischen Wissenschaften, Springer-Verlag, 1976.
- [16] G. Fichera, Unilateral constraints in elasticity, Actes, Congres international de Mathematiques 3 (1970), 79-84.
- [17] A. Friedman, Boundary behavior of solutions of variational inequalities for elliptic operators, Arch. Rational Mech. Anal. 27 (1967), 95-107.
- [18] D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Classics in Mathematics, 2nd ed., Springer-Verlag, Berlin-Heidelberg, 2001.
- [19] D. Kinderlehrer, Remarks about Signorini's problem in linear elasticity, Ann. Sc. Norm. Super. Pisa 8 (1981) 4, 605-645.
- [20] D. Kinderlehrer, G. Stampacchia, An introduction to variational inequalities and their applications, volume 31 ol SIAM's classics in applied mathematics, Society for Industrial and Applied Mathematics, Philadelphia, 2000.
- [21] J.L. Lions, G. Stampacchia, Variational inequalities, Comm. Pure Appl. Math. 20 (1967) 3, 493-519.
- [22] A. Petrosyan, H. Shahgholian, N. Uraltseva, Regularity of Free Boundaries in Obstacle-Type Problems, vol. 136, Graduate Studies in Mathematics, American Mathematical Society, 2012.
- [23] M. Schatzmann, Problemes aux limites non lineaires non coercifs, Ann. Sc. Norm. Super. Pisa Cl. Sci. 27 (1973), 1-686.
- [24] A. Signorini, Questioni di elasticitd non linearizzata e semilinearizzata, Rend. Mat. Appl. 18 (1959), 95-139.
- [25] R.P. Sperb, Maximum Principles and Their Applications, Mathematics in Science and Engineering, Academic Press, 1981.
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Bibliografia
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