
Mathematics in Engineering, 2020, 2(4): 698708. doi: 10.3934/mine.2020032
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Remarks on the decay/growth rate of solutions to elliptic free boundary problems of obstacle type
1 Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran
2 Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden
3 Department of Mathematics, University of DuisburgEssen, Essen, Germany
^{†}This contribution is part of the Special Issue: Contemporary PDEs between theory and modeling—Dedicated to Sandro Salsa, on the occasion of his 70th birthday
Guest Editor: Gianmaria Verzini
Link: www.aimspress.com/mine/article/5753/specialarticles
Received: , Accepted: , Published:
Special Issues: Contemporary PDEs between theory and modeling—Dedicated to Sandro Salsa, on the occasion of his 70th birthday
References
1. Andersson J, Lindgren E, Shahgholian H (2013) Optimal regularity for the nosign obstacle problem. Commun Pure Appl Math 66: 245262.
2. Caffarelli LA (1998) The obstacle problem revisited. J Fourier Anal Appl 4: 383402.
3. Figalli A, Shahgholian H (2014) A general class of free boundary problems for fully nonlinear elliptic equations. Arch Ration Mech Anal 213: 269286.
4. Gilbarg D, Trudinger NS (2001) Elliptic Partial Differential Equations of Second Order, Springer.
5. Krylov NV (1999) Weighted Sobolev spaces and Laplace's equation and the heat equations in a half space. Commun Part Diff Eq 24: 16111653.
6. Petrosyan A, Shahgholian H, Uraltseva N (2012) Regularity of Free Boundaries in ObstacleType Problems, Providence: American Mathematical Society.
7. Rákosník J (1989) On embeddings and traces in Sobolev spaces with weights of power type, In: Approximation and Function Spaces, Warsaw: Banach Center Publ., 331339.
8. Shahgholian H (2003) C^{1,1} regularity in semilinear elliptic problems, Commun Pure Appl Math 56: 278281.
9. Shahgholian H, Yeressian K (2017) The obstacle problem with singular coefficients near Dirichlet data, Ann Inst H Poincaré Anal Non Linéaire 34: 293334.
10. Weiss GS (2001) An obstacleproblemlike equation with two phases: pointwise regularity of the solution and an estimate of the Hausdorff dimension of the free boundary. Interface Free Bound 3: 121128.
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