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A result on singularly perturbed elliptic problems
On the pointwise jump condition at the free boundary in the 1phase Stefan problem
1.  Department of Mathematics, Purdue University, United States 
2.  Department of Mathematics, Kansas State University, Manhattan, KS 66506, United States 
[1] 
Luigi Ambrosio, Michele Miranda jr., Diego Pallara. Sets with finite perimeter in Wiener spaces, perimeter measure and boundary rectifiability. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 591606. doi: 10.3934/dcds.2010.28.591 
[2] 
Alessandro Ferriero, Nicola Fusco. A note on the convex hull of sets of finite perimeter in the plane. Discrete and Continuous Dynamical Systems  B, 2009, 11 (1) : 103108. doi: 10.3934/dcdsb.2009.11.103 
[3] 
Chaoxu Pei, Mark Sussman, M. Yousuff Hussaini. A spacetime discontinuous Galerkin spectral element method for the Stefan problem. Discrete and Continuous Dynamical Systems  B, 2018, 23 (9) : 35953622. doi: 10.3934/dcdsb.2017216 
[4] 
Chifaa Ghanmi, Saloua Mani Aouadi, Faouzi Triki. Recovering the initial condition in the onephase Stefan problem. Discrete and Continuous Dynamical Systems  S, 2022, 15 (5) : 11431164. doi: 10.3934/dcdss.2021087 
[5] 
Fanghua Lin, Dan Liu. On the Betti numbers of level sets of solutions to elliptic equations. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 45174529. doi: 10.3934/dcds.2016.36.4517 
[6] 
Marianne Korten, Charles N. Moore. Regularity for solutions of the twophase Stefan problem. Communications on Pure and Applied Analysis, 2008, 7 (3) : 591600. doi: 10.3934/cpaa.2008.7.591 
[7] 
Michael L. Frankel, Victor Roytburd. A Finitedimensional attractor for a nonequilibrium Stefan problem with heat losses. Discrete and Continuous Dynamical Systems, 2005, 13 (1) : 3562. doi: 10.3934/dcds.2005.13.35 
[8] 
Adriana C. Briozzo, María F. Natale, Domingo A. Tarzia. The Stefan problem with temperaturedependent thermal conductivity and a convective term with a convective condition at the fixed face. Communications on Pure and Applied Analysis, 2010, 9 (5) : 12091220. doi: 10.3934/cpaa.2010.9.1209 
[9] 
Qingjie Hu, Zhihao Ge, Yinnian He. Discontinuous Galerkin method for the Helmholtz transmission problem in twolevel homogeneous media. Discrete and Continuous Dynamical Systems  B, 2020, 25 (8) : 29232948. doi: 10.3934/dcdsb.2020046 
[10] 
Mario Roldan. Hyperbolic sets and entropy at the homological level. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 34173433. doi: 10.3934/dcds.2016.36.3417 
[11] 
Michael L. Frankel, Victor Roytburd. Fractal dimension of attractors for a Stefan problem. Conference Publications, 2003, 2003 (Special) : 281287. doi: 10.3934/proc.2003.2003.281 
[12] 
Lincoln Chayes, Inwon C. Kim. The supercooled Stefan problem in one dimension. Communications on Pure and Applied Analysis, 2012, 11 (2) : 845859. doi: 10.3934/cpaa.2012.11.845 
[13] 
Piotr B. Mucha. Limit of kinetic term for a Stefan problem. Conference Publications, 2007, 2007 (Special) : 741750. doi: 10.3934/proc.2007.2007.741 
[14] 
Marvin S. Müller. Approximation of the interface condition for stochastic Stefantype problems. Discrete and Continuous Dynamical Systems  B, 2019, 24 (8) : 43174339. doi: 10.3934/dcdsb.2019121 
[15] 
Jan Prüss, Jürgen Saal, Gieri Simonett. Singular limits for the twophase Stefan problem. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 53795405. doi: 10.3934/dcds.2013.33.5379 
[16] 
Karl P. Hadeler. Stefan problem, traveling fronts, and epidemic spread. Discrete and Continuous Dynamical Systems  B, 2016, 21 (2) : 417436. doi: 10.3934/dcdsb.2016.21.417 
[17] 
Gyula Csató. On the isoperimetric problem with perimeter density $r^p$. Communications on Pure and Applied Analysis, 2018, 17 (6) : 27292749. doi: 10.3934/cpaa.2018129 
[18] 
Hayk Mikayelyan, Henrik Shahgholian. Convexity of the free boundary for an exterior free boundary problem involving the perimeter. Communications on Pure and Applied Analysis, 2013, 12 (3) : 14311443. doi: 10.3934/cpaa.2013.12.1431 
[19] 
Everaldo S. de Medeiros, Jianfu Yang. Asymptotic behavior of solutions to a perturbed pLaplacian problem with Neumann condition. Discrete and Continuous Dynamical Systems, 2005, 12 (4) : 595606. doi: 10.3934/dcds.2005.12.595 
[20] 
Christina A. Hollon, Jeffrey T. Neugebauer. Positive solutions of a fractional boundary value problem with a fractional derivative boundary condition. Conference Publications, 2015, 2015 (special) : 615620. doi: 10.3934/proc.2015.0615 
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