On the two-phase membrane problem with coefficients below the Lipschitz threshold

Erik Lindgren; Henrik Shahgholian; Anders Edquist

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 6, page 2359-2372
  • ISSN: 0294-1449

How to cite

top

Lindgren, Erik, Shahgholian, Henrik, and Edquist, Anders. "On the two-phase membrane problem with coefficients below the Lipschitz threshold." Annales de l'I.H.P. Analyse non linéaire 26.6 (2009): 2359-2372. <http://eudml.org/doc/78937>.

@article{Lindgren2009,
author = {Lindgren, Erik, Shahgholian, Henrik, Edquist, Anders},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {obstacle problem; elliptic equation; regularity; free boundary},
language = {eng},
number = {6},
pages = {2359-2372},
publisher = {Elsevier},
title = {On the two-phase membrane problem with coefficients below the Lipschitz threshold},
url = {http://eudml.org/doc/78937},
volume = {26},
year = {2009},
}

TY - JOUR
AU - Lindgren, Erik
AU - Shahgholian, Henrik
AU - Edquist, Anders
TI - On the two-phase membrane problem with coefficients below the Lipschitz threshold
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 6
SP - 2359
EP - 2372
LA - eng
KW - obstacle problem; elliptic equation; regularity; free boundary
UR - http://eudml.org/doc/78937
ER -

References

top
  1. [1] Alt Hans Wilhelm, Caffarelli Luis A., Friedman Avner, Variational problems with two phases and their free boundaries, Trans. Amer. Math. Soc.282 (2) (1984) 431-461. Zbl0844.35137MR732100
  2. [2] Agmon S., Douglis A., Nirenberg L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II, Comm. Pure Appl. Math.17 (1964) 35-92. Zbl0123.28706MR162050
  3. [3] Blank Ivan, Sharp results for the regularity and stability of the free boundary in the obstacle problem, Indiana Univ. Math. J.50 (3) (2001) 1077-1112. Zbl1032.35170MR1871348
  4. [4] Blank Ivan, Shahgholian Henrik, Boundary regularity and compactness for overdetermined problems, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)2 (4) (2003) 787-802. Zbl1170.35484MR2040643
  5. [5] Caffarelli L.A., The obstacle problem revisited, J. Fourier Anal. Appl.4 (4–5) (1998) 383-402. Zbl0928.49030MR1658612
  6. [6] Caffarelli Luis A., Jerison David, Kenig Carlos E., Some new monotonicity theorems with applications to free boundary problems, Ann. of Math. (2)155 (2) (2002) 369-404. Zbl1142.35382MR1906591
  7. [7] David Guy, Kenig Carlos, Toro Tatiana, Asymptotically optimally doubling measures and Reifenberg flat sets with vanishing constant, Comm. Pure Appl. Math.54 (4) (2001) 385-449. Zbl1031.28004MR1808649
  8. [8] Edquist Anders, Lindgren Erik, A two-phase obstacle-type problem for the p-laplacian, Calc. Var. Partial Differential Equations35 (4) (2009) 421-433. Zbl1177.35259MR2496650
  9. [9] Kinderlehrer D., Nirenberg L., Spruck J., Regularity in elliptic free boundary problems, J. Anal. Math.34 (1978/1979) 86-119. Zbl0402.35045MR531272
  10. [10] Kinderlehrer David, Stampacchia Guido, An Introduction to Variational Inequalities and Their Applications, Pure Appl. Math., vol. 88, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1980. Zbl0457.35001MR567696
  11. [11] Reifenberg E.R., Solution of the Plateau problem for m-dimensional surfaces of varying topological type, Acta Math.104 (1960) 1-92. Zbl0099.08503MR114145
  12. [12] Shahgholian Henrik, C 1 , 1 regularity in semilinear elliptic problems, Comm. Pure Appl. Math.56 (2) (2003) 278-281. Zbl1258.35098MR1934623
  13. [13] Shahgholian Henrik, Uraltseva Nina, Weiss Georg S., Global solutions of an obstacle-problem-like equation with two phases, Monatsh. Math.142 (1–2) (2004) 27-34. Zbl1057.35098MR2065019
  14. [14] Shahgholian Henrik, Uraltseva Nina, Weiss Georg S., The two-phase membrane problem—Regularity of the free boundaries in higher dimensions, Int. Math. Res. Not. IMRN8 (2007), Art. ID rnm026, 16 pp. Zbl1175.35157MR2340105
  15. [15] Uraltseva N.N., Two-phase obstacle problem, Function theory and phase transitions, J. Math. Sci. (N. Y.)106 (3) (2001) 3073-3077. MR1906034
  16. [16] Weiss G.S., An obstacle-problem-like equation with two phases: Pointwise regularity of the solution and an estimate of the Hausdorff dimension of the free boundary, Interfaces Free Bound.3 (2) (2001) 121-128. Zbl0986.35139MR1825655
  17. [17] Widman Kjell-Ove, Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations, Math. Scand.21 (1967/1968) 17-37. Zbl0164.13101MR239264

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.