Open Access
Volume 29, 2023
Article Number 30
Number of page(s) 23
Published online 27 April 2023
  1. Y. Achdou, An inverse problem for a parabolic variational inequality arising in volatility calibration with American options. SIAM J. Control Optim. 43 (2005) 1583–1615. [Google Scholar]
  2. Y. Achdou, An inverse problem for a parabolic variational inequality with an integro-differential operator. SIAM J. Control Optim. 47 (2008) 733–767. [Google Scholar]
  3. A. Alphonse, M. Hintermüller and C.N. Rautenberg, Stability of the solution set of quasi-variational inequalities and optimal control. SIAM J. Control Optim. 58 (2020) 3508–3532. [Google Scholar]
  4. A. Alphonse, M. Hintermüller and C.N. Rautenberg, Directional differentiability for elliptic quasi-variational inequalities of obstacle type. Calc. Var. Partial Diff. Equ. 58 (2019) 47. [Google Scholar]
  5. J.P. Aubin and A. Cellina, Differential Inclusions. Springer-Verlag, Berlin (1984). [CrossRef] [Google Scholar]
  6. D. Aussel, K.C. Van and D. Salas, Quasi-variational inequality problems over product sets with quasi-monotone operators. SIAM J. Optim. 29 (2019) 1558–1577. [Google Scholar]
  7. P. Baroni, M. Colombo and G. Mingione, Harnack inequalities for double phase functionals. Nonlinear Anal. 121 (2015) 206–222. [Google Scholar]
  8. P. Baroni, M. Colombo and G. Mingione, Regularity for general functionals with double phase. Calc. Var. Partial Diff. Equ. 57 (2018) 48. [Google Scholar]
  9. B.M. Brown, M. Jais and I.W. Knowles, A variational approach to an elastic inverse problem. Inverse Probl. 21 (2005) 1953–1973. [Google Scholar]
  10. S.-S. Byun, J. Oh, Regularity results for generalized double phase functionals. Anal. PDE 13 (2020) 1269–1300. [CrossRef] [MathSciNet] [Google Scholar]
  11. S. Carl and V.K. Le, Multi-valued Variational Inequalities and Inclusions. Springer, Cham (2021). [CrossRef] [Google Scholar]
  12. S. Carl, V.K. Le and D. Motreanu, Nonsmooth Variational Problems and Their Inequalities. Springer, New York (2007). [CrossRef] [Google Scholar]
  13. S. Carl, V.K. Le and P. Winkert, Multi-valued variational inequalities for variable exponent double phase problems: comparison and extremality results, Adv. Differential Equations, accepted 2023. [Google Scholar]
  14. C. Clason, A.A. Khan, M. Sama and C. Tammer, Contingent derivatives and regularization for noncoercive inverse problems. Optimization 68 (2019) 1337–1364. [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Colombo and G. Mingione, Bounded minimisers of double phase variational integrals. Arch. Ration. Mech. Anal. 218 (2015) 219–273. [Google Scholar]
  16. M. Colombo and G. Mingione, Regularity for double phase variational problems. Arch. Ration. Mech. Anal. 215 (2015) 443–496. [Google Scholar]
  17. Á. Crespo-Blanco, L. Gasiński, P. Harjulehto and P. Winkert, A new class of double phase variable exponent problems: existence and uniqueness. J. Diff. Equ. 323 (2022) 182–228. [Google Scholar]
  18. F. Facchinei and J.-S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems, Vols. I and II. Springer, New York (2003). [Google Scholar]
  19. L. Gasiñski and P. Winkert, Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold. J. Diff. Equ. 274 (2021) 1037–1066. [Google Scholar]
  20. J. Gwinner, An optimization approach to parameter identification in variational inequalities of second kind. Optim. Lett. 12 (2018) 1141–1154. [Google Scholar]
  21. J. Gwinner, B. Jadamba, A.A. Khan and M. Sama, Identification in variational and quasi-variational inequalities. J. Convex Anal. 25 (2018) 545–569. [Google Scholar]
  22. M. Hintermuüller and A. Laurain, Optimal shape design subject to elliptic variational inequalities. SIAM J. Control Optim. 49 (2011) 1015–1047. [Google Scholar]
  23. M. Hintermuüller and C.N. Rautenberg, A sequential minimization technique for elliptic quasi-variational inequalities with gradient constraints. SIAM J. Optim. 22 (2012) 1224–1257. [Google Scholar]
  24. S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis, Vol. I. Kluwer Academic Publishers, Dordrecht (1997). [CrossRef] [Google Scholar]
  25. S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis, Vol. II. Kluwer Academic Publishers, Dordrecht (2000). [CrossRef] [Google Scholar]
  26. A. Iannizzotto and N.S. Papageorgiou, Existence of three nontrivial solutions for nonlinear Neumann hemivariational inequalities. Nonlinear Anal. 70 (2009) 3285–3297. [Google Scholar]
  27. C. Kanzow and D. Steck, Quasi-variational inequalities in Banach spaces: theory and augmented Lagrangian methods. SIAM J. Optim. 29 (2019) 3174–3200. [Google Scholar]
  28. A. Lê, Eigenvalue problems for the p-Laplacian. Nonlinear Anal. 64 (2006) 1057–1099. [Google Scholar]
  29. W. Liu and G. Dai, Existence and multiplicity results for double phase problem. J. Diff. Equ. 265 (2018) 4311–4334. [Google Scholar]
  30. Z. Liu, S. Zeng and D. Motreanu, Partial differential hemivariational inequalities. Adv. Nonlinear Anal. 7 (2018) 571–586. [Google Scholar]
  31. P. Marcellini, Regularity and existence of solutions of elliptic equations with p, q-growth conditions. J. Diff. Equ. 90 (1991) 1–30. [Google Scholar]
  32. P. Marcellini, Regularity of minimizers of integrals of the calculus of variations with nonstandard growth conditions. Arch. Rational Mech. Anal. 105 (1989) 267–284. [Google Scholar]
  33. S. Migórski, A.A. Khan and S. Zeng, Inverse problems for nonlinear quasi-hemivariational inequalities with application to mixed boundary value problems. Inverse Probl. 36 (2020) 20. [Google Scholar]
  34. S. Migórski, A.A. Khan and S. Zeng, Inverse problems for nonlinear quasi-variational inequalities with an application to implicit obstacle problems of p-Laplacian type. Inverse Probl. 35 (2019) 035004. [Google Scholar]
  35. S. Migórski and A. Ochal, An inverse coefficient problem for a parabolic hemivariational inequality. Appl. Anal. 89 (2010) 243–256. [Google Scholar]
  36. S. Migórski, A. Ochal and M. Sofonea, Nonlinear Inclusions and Hemivariational Inequalities. Springer, New York (2013). [CrossRef] [Google Scholar]
  37. G. Mingione and V. Rädulescu, Recent developments in problems with nonstandard growth and nonuniform ellipticity. J. Math. Anal. Appl. 501 (2021) 125197. [Google Scholar]
  38. P.D. Panagiotopoulos, Nonconvex problems of semipermeable media and related topics. Z. Angew. Math. Mech. 65 (1985) 29–36. [Google Scholar]
  39. P.D. Panagiotopoulos, Hemivariational Inequalities. Springer-Verlag, Berlin (1993). [CrossRef] [Google Scholar]
  40. J.S. Pang, A degree-theoretic approach to parametric nonsmooth equations with multivalued perturbed solution sets. Math. Program. 62 (1993) 359–383. [CrossRef] [Google Scholar]
  41. J.-S. Pang and D. Stewart, Differential variational inequalities. Math. Program,. 113 (2008) 345–424. [CrossRef] [MathSciNet] [Google Scholar]
  42. J.-S. Pang and D. Stewart, Solution dependence on initial conditions in differential variational inequalities. Math. Program,. 116 (2009) 429–460. [CrossRef] [MathSciNet] [Google Scholar]
  43. N.S. Papageorgiou, V.D. Radulescu and D.D. Repovs, Nonhomogeneous hemivariational inequalities with indefinite potential and Robin boundary condition. J. Optim. Theory Appl. 175 (2017) 293–323. [Google Scholar]
  44. N.S. Papageorgiou and C. Vetro, Existence and relaxation results for second order multivalued systems. Acta Appl. Math. 173 (2021) 36. [Google Scholar]
  45. N.S. Papageorgiou and P. Winkert, Applied Nonlinear Functional Analysis. An Introduction. De Gruyter, Berlin (2018). [CrossRef] [Google Scholar]
  46. M.A. Ragusa and A. Tachikawa, Regularity for minimizers for functionals of double phase with variable exponents. Adv. Nonlinear Anal. 9 (2020) 710–728. [Google Scholar]
  47. J. Simon, Régularité de la solution d’une équation non linéaire dans RN. Journées d’Analyse Non Linéaire (Proc. Conf. Besançon, 1977). Springer, Berlin 665 (1978) 205–227. [Google Scholar]
  48. S. Zeng, Y. Bai, L. Gasinński and P. Winkert, Convergence analysis for double phase obstacle problems with multivalued convection term. Adv. Nonlinear Anal. 10 (2021) 659–672. [Google Scholar]
  49. S. Zeng, Y. Bai, L. Gasinński and P. Winkert, Existence results for double phase implicit obstacle problems involving multivalued operators. Calc. Var. Partial Diff. Equ. 59 (2020) 18. [Google Scholar]
  50. S. Zeng, L. Gasinński, P. Winkert and Y. Bai, Existence of solutions for double phase obstacle problems with multivalued convection term. J. Math. Anal. Appl. 501 (2021) 123997. [Google Scholar]
  51. S. Zeng, V.D. Rădulescu and P. Winkert, Double phase implicit obstacle problems with convection and multivalued mixed boundary value conditions. SIAM J. Math. Anal. 54 (2022) 1898–1926. [Google Scholar]
  52. V.V. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory. Izv. Akad. Nauk SSSR Ser. Mat. 50 (1986) 675–710. [Google Scholar]
  53. V.V. Zhikov, On Lavrentiev’s phenomenon. Russian J. Math. Phys. 3 (1995) 249–269. [Google Scholar]
  54. V.V. Zhikov, On variational problems and nonlinear elliptic equations with nonstandard growth conditions. J. Math. Sci. 173 (2011) 463–570. [Google Scholar]

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