PDE & Potential Theory Group Analysis Group Activities
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Publications / Preprints

65) Uniform regularity close to cross singularities in an unstable free boundary problem, with J. Andersson, and G. Weiss.  Submitted.

64) On the two-phase membrane problem with coefficients below Lipschitz threshold. Joint with A: Edquist, and E. Lindgren.  Ann. Inst. H. Poincaré Anal. Non Linéaire (To appear)

63)   A PDE approach to regularity of solutions to finite horizon optimal switching problmes, (with T. Arnarsson, B. Djehiche, M. Poghosyan),  Nonlinear Analysis, to appear.

62)   A parabolic  two-phase obstacle-like  equation, joint with Nina Uraltseva, and G. S. Weiss, Adv in Math., to appear.

61)   Growth estimates through scaling for quasilinear  partial differential equations, with Tero Kilpel¨ainen, Henrik Shahgholian, and Xiao Zhong. Ann. Acad. Sci. Fenn. Math. 32 (2007), no. 2, 595--599.

60)   Parabolic obstacle problems applied to finance: free-boundary-regularity approach, with A. Petrosyan, appendix by T. Arnarson, Recent Developments in Nonlinear Partial Differential Equations, Contemporary Matematics 439 (2007), 117--133.

59)   The two-phase membrane problem- regularity of the free boundary in higher dimensions   (Joint with N. Uraltseva and G.S. Weiss) Int. Math. Res. Not. IMRN 2007, no. 8,

58)   Convexity of the free boundary for an exterior free boundary problem involving the perimeter,    (Joint with Hayk Mikaelyan)

57)   Geometric and energetic criteria for the free boundary regularity in an obstacle-type problem  (Joint with A. Petrosyan) Amer. J. Math. 129 (2007), no. 6, 1659--1688.

56)   Aleksandrov and Kelvin Reflection and the Regularity of Free Boundaries   (Joint with G.S. Weiss,) Internat. Ser. Numer. Math., 154, Birkhäuser, Basel, 2007

55) The Two-Phase Membrane Problem -an Intersection-Comparison Approach to the Regularity at Branch Points (Joint with G.S. Weiss) Adv. Math. 205 (2006), no. 2, 487--503.

54) Convex configurations for solutions to semilinear elliptic problems in convex rings (Joint with Andrew Acker and Mikayel Poghosyan) Comm. Partial Differential Equations 31 (2006), no. 7-9, 1273--1287.

53) Free boundary regularity close  to initial state for parabolic obstacle problem Trans. Amer. Math. Soc. 360 (2008), no. 4, 2077--2087.

52) The singular set for the composite membrane problem . Comm. Math. Phys. 271 (2007), no. 1, 93--101.

51) Gamma limits in some Bernoulli free boundary problem (Joint with Bernd Kawohl)
Archive der Mathematik 84 (2005)

50) When Does the Free boundary enter into corner points of the fixed boundary ? (Nina Uraltseva Festschrift: Zap. Nauchn. Sem. S.-Petersburg. Otdel. Mat. Inst. Steklov.) POMI, Tin press

49) The structure of the singular set of a free boundary in potential theory
(Joint with Luis Caffarelli). Journal of Contemporary  Mathematical Analysis;  Izvestiya Nationalnoi Akademii Nauk Armenii. Matematika

48) Quadrature domains and Brownian motion (Harold Shapiro Festschrift, to appear.)

47) Global Solutions of the Obstacle Problem in Half-spaces, and their impact on Local Stability (Joint With John Andersson).
 Cal. Var. Partial Differential Equations

46) The behavior of the Free Boundary near the fixed boundary for  a minimization problem (Joint with A. Karakhanyan, and C. Kenig)
Cal. Var. Partial Differential Equations

45) Non-convexity of level sets in convex rings for semilinear elliptic problems
(Joint with R. Monneau) Indiana Univ. Math. J. 54 No. 2 (2005), 465-472

44) Uniform and tangential approximation on a stripe by entire functions, having optimal growth (Joint with N. Arakelian) Comput. Methods Funct. Theory, 3 (2003), no. 1-2, 359--383

43) Lipschitz property of the free boundary in the  parabolic obstacle problem (Joint with D. Apushkinskaya and N. Uraltseva) Algebra i Analiz, vol 15 (2003),  No 3

42) Global solutions of an obstacle-problem-like equation with two phases
(Joint with N. Uraltseva and G.S. Weiss) Monatshefte fur Matematik

41) Regularity of a free boundary in parabolic potential theory (Joint with L. Caffarelli and Arshak Petrosyan) J. Amer. Math. Soc., 17 (2004), no. 4, 827--869

40) Free boundary regularity for a problem arising in Superconductivity (Joint with L. Caffarelli and J. Salazar, Arch. Ration. Mech. Anal., 171 (2004) no. 1, 115--128.

39) The multi-layer free boundary problem for the $p$-Laplacian in convex domains (Joint with Andrew Acker, Antoine Henrot and Mikayel Poghosyan)
Interfaces and Free boundary

38) Boundary Regularity and Compactness for Overdetermined Problems (Joint with I. Blank) 4-th issue, vol. 2/2003 Annali Scuola Normale Superiore-Classe di Scienze, 787-802

37) $C^{1,1}$-regularity in semilinear elliptic problems Comm. Pure Appl. Math. 56 (2003), no. 2, 278--281.

36) Uniqueness of a free boundary problem of $p$-parabolic type (Joint with Aram Hakobyan) Journal of Contemporary Mathematical Analysis, vol. 36, No. 5, 2001, pp. 12-18

35) Generalized mean value property for caloric functions (Survey) (Joint with Aram Hakobyan) Proceeding 3rd International ISAAC Congress, Vol. II, 891-895

34) On the global solutions of the parabolic obstacle problem (Joint with D. E. Apushkinskaya, N. N. Uraltseva) Algebra i Analiz 14 (2002), no. 1, 3--25.

33) An overdetermined problem in nonlinear parabolic potential theory; Uniqueness (Joint with A. Hakobyan) Potential Analysis volume 21, no. 4 (December 2004).

32) Singular perturbation of a free boundary for the $p$-Laplacian (Joint with D. Danielli, A. Petrosyan) Indiana Univ. Math. J., 52 (2003) no. 2, 457--476.

31) Hausdorff dimension and stability of the $p$-obstacle problem $(2 < p )$ (Joint with Ki-Ahm Lee) J. Differential Equations, 195 (2003), no. 1, 14--24.

30) Analysis of the free boundary for the $p$-parabolic variational problem
Revista Matematica Iberoamericana

29) Boundary estimates for solutions to the parabolic free boundary problem (Joint with Darya Apushkinskaya and Nina Uraltseva) Zap. Nauchn. Sem. S.-Petersburg. Otdel. Mat. Inst. Steklov. (POMI) 271 (2000), Kraev. Zadachi Mat. Fiz. i Smezh. Vopr. Teor. Funkts. 31, 39--55, 313.

28) On Phragmen Lindelof Principle (Joint with Ashot Vagharshakyan) Complex Variables Theory Appl. 46 (2001), no. 4, 295--305

27) A free boundary problem for infinite Laplace equation (Joint with Arshak Petrosyan and Juan Manfredi) Calc. Var. Partial Differential Equations 14 (2002), no. 3, 359--384.

26) The one phase free boundary problem for the $p$-Laplacian with non-constant Bernoulli boundary condition (Joint with A. Henrot) Trans. Amer. Math. Soc. 354 (2002), no. 6, 2399--2416

25) Regularity properties of a free boundary near contact points with the fix boundary (Joint with N. Uraltseva) Duke Math. J. 116 (2003), no. 1, 1--34

24) The impact of monotonicity formulas in regularity of free boundaries (A survey article) Proceeding of 3d European Math. Congress.

23) Regularity of a free boundary for viscosity solutions of nonlinear elliptic equations (Joint with K. Lee) Comm. on Pure and Applied Mathematics, Vol. LIV, 0001--0014 (2001).

22) Optimal growth of functions with bounded Laplacian (Joint with L. Karp) Electron. J. Diff. Eqns., Vol. 2000 (2000), No. 03, pp. 1-9.

21) Regularity of a free boundary at the infinity point (Joint with L. Karp) Comm. Partial Differential Equations 25 (2000), no. 11-12, 2055--2086.

20) Regularity of a free boundary in potential theory with application to the Pompeiu problem (Joint with L. Caffarelli and L. Karp) Ann. of Math. (2) 151 (2000), no. 1, 269--292.

19) On the porosity of free boundaries in degenerate variational inequalities (Joint with L. Karp and T. Kilpeläinen, A. Petrosyan) J. Differential Equations 164 (2000), no. 1, 110--117.

18) Existence of classical solutions to a free boundary problem for the p-Laplace operator: (II) the interior convex case (Joint with A. Henrot) Indiana Univ. Math. J. 49 (2000), no. 1, 311--323

17) Existence of classical solutions to a free boundary problem for the p-Laplace operator: (I) the exterior convex case (Joint with A. Henrot) J. Reine Angew. Math. 521 (2000), 85--97

16) Dense subsets of $L^1$-solutions to elliptic partial differential equations J. Approx. Theory 102 (2000), no. 2, 189--216.

15) Two related minimum problems with free boundaries governed by the $p$-Laplace operator (Joint with H. Hosseinzadeh, Mazandaran Univ.) J. Sci. Univ. Tehran Int. Ed. 3 (1998), no. 2, 123--137. 35J60 (35R35)

14) Regularity of a free boundary problem (Joint with Lavi Karp) J. Geom. Anal. 9 (1999), no. 4, 653--669

13) Propagation of smallness for harmonic and analytic functions in arbitrary domains (Joint with N. Arakelian, Armenian Academy of Sciences) Bull. London Math. Soc. 31 (1999) 1--8

12) Some qualitative aspects of a free boundary problem for the p-Laplace operator (Joint with H. Hosseinzadeh,) Ann. Acad. Sci. Fenn. Math. 24 (1999), no. 1, 109--121.

11) Uniqueness in an overdetermined boundary value problem for the p-Laplacian (Joint with F. Bahrami) Proc. Amer. Math. Soc. 126 (1998), no. 3, 745--750

10) Convexity of free boundaries with Bernoulli type boundary condition (Joint work with A. Henrot, Besancon, France) Nonlinear Analysis T.M.A., vol 28, no 5 (1997), pp 815-823.

9) Existence and geometric properties of solutions of a free boundary problem in potential theory, (Joint with B. Gustafsson, KTH) J. Reine Angew. Math. 473 (1996), 137-179

8) Qualitative properties of positive solutions to nonlinear PDE and FBP Nonlinear Anal. T.M.A. vol 27, (7) pp. 801-809, 1996

7) Existence of quadrature surfaces for positive Dirac masses Potential Anal. 3(1994) pp 245-255

6) Convexity and uniqueness in an inverse problem of potential theory, Proc. Amer. Math. Soc. 116(1992) pp 1097-1099

5) A characterization of the sphere in terms of single-layer potentials, Proc. Amer. Math. Soc. 115(1992) pp 1167-1168

4) Quadrature surfaces as free boundaries, Ark. Mat. Vol 32, nr. 2, (1994).

3) On the Newtonian potential of a heterogeneous ellipsoid, SIAM J. Math. Anal. Vol. 22, nr. 5 (1991), pp 1246-1255

2) On quadrature domains and the Schwarz potential J. of Math. Anal. and Appl. 171 (1992) pp 61-78.

1) Unbounded quadrature domains in R^n J. Anal. Math. Vol. 56 (1991) pp 281-291.

Henrik Shahgholian's home page

Updated on 26 January, 2007.