Oblique derivative problems and invariant measures

I. Capuzzo Dolcetta; M. G. Garroni

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1986)

  • Volume: 13, Issue: 4, page 689-720
  • ISSN: 0391-173X

How to cite

top

Capuzzo Dolcetta, I., and Garroni, M. G.. "Oblique derivative problems and invariant measures." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 13.4 (1986): 689-720. <http://eudml.org/doc/83994>.

@article{CapuzzoDolcetta1986,
author = {Capuzzo Dolcetta, I., Garroni, M. G.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {second-order oblique derivative; Hölder continuous; unilateral problem; stochastic processes; singularity; Dirichlet boundary data; uniqueness; smooth domain},
language = {eng},
number = {4},
pages = {689-720},
publisher = {Scuola normale superiore},
title = {Oblique derivative problems and invariant measures},
url = {http://eudml.org/doc/83994},
volume = {13},
year = {1986},
}

TY - JOUR
AU - Capuzzo Dolcetta, I.
AU - Garroni, M. G.
TI - Oblique derivative problems and invariant measures
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1986
PB - Scuola normale superiore
VL - 13
IS - 4
SP - 689
EP - 720
LA - eng
KW - second-order oblique derivative; Hölder continuous; unilateral problem; stochastic processes; singularity; Dirichlet boundary data; uniqueness; smooth domain
UR - http://eudml.org/doc/83994
ER -

References

top
  1. [1] R. Adams, Sobolev spaces, Academic Press, New York, 1975. Zbl0314.46030MR450957
  2. [2] S. Agmon - A. Douglis - L. Nirenberg, Estimates near the boundary for solutions of elliptic PDE'S, Comm. Pure Appl. Math., 12 (1959), pp. 623-727. Zbl0093.10401MR125307
  3. [3] A. Bensoussan - J.L. Lions, Contrôle impulsionnel et inequations quasi-variationnelles, Dunod, Paris, 1982. Zbl0491.93002MR673169
  4. [4] A. Bensoussan - J.L. Lions, On the asymptotic behaviour of the solution of variational inequalities, in « Summer School on the Theory of Nonlinear Operators », Akademic Verlag, Berlin, (1978), pp. 25-40. Zbl0437.49014MR540445
  5. [5] A. Bensoussan - J.L. Lions - G. Papanicolau, Asymptotic analysis for periodic structures, North Holland, Amsterdam, 1978. Zbl0404.35001MR503330
  6. [6] I. Capuzzo Dolcetta - M. Lorenzani - F. Spizzichino, A degenerate complementarity system and applications to the optimal stopping of Markov chains, Boll. Un. Mat. Ital., (5) 17-B (1980), pp. 692-703. Zbl0439.60039MR580550
  7. [7] I. Capuzzo Dolcetta - M.G. Garroni, Comportement asymptotique de la solution de problèmes non sous forme divergence avec condition de derivee oblique sur le bord, C.R.A.S., Paris, t. 299, S. I, n. 17, 1984, pp. 843-846. Zbl0574.35028MR777744
  8. [8] M. Chicco, Third boundary value problem in H2,p(Ω) for a class of linear second order elliptic partial differential equations, Rend. Ist. Mat. Univ. Trieste, 4 (1972), pp. 80-94. Zbl0245.35028
  9. [9] J.L. DooB, Stochastic Processes, J. Wiley, New York, 1953. Zbl0053.26802MR58896
  10. [10] A. Friedman, Asymptotic stability of solutions of parabolic equations under various boundary conditions, Technical Report No. 6, Dpt. of Math. Univ. of California, Berkeley, 1959. 
  11. [11] M.G. Garroni, Regularity of a nonlinear variational inequality with obstacle on the boundary, Analisi Funzionale e Applicazioni, Suppl. Boll. Un. Mat. Ital. Vol. I (1980), pp. 267-286. Zbl0446.35023MR677702
  12. [12] M.G. Garroni - J.L. Menaldi, Green function and invariant density for an integro-differential operator of second order, Part I, to appear, announced in C.R.A.S., 1986. MR872559
  13. [13] M.G. Garroni - V.A. Solonnikov, On parabolic oblique derivative problems-with Hölder continuous coefficients, Comm. on PDE, Vol. 9, No. 14 (1984), pp. 1323-1373. Zbl0562.35044MR765964
  14. [14] O.H. Ladyzhenskaya - V.A. Solonnikov - N.N. Uraltseva, Linear and quasilinear equations of parabolic type, Nauka, Moscow, 1967. Zbl0164.12302
  15. [15] P.L. Lions - A.S. Snitzman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure and Appl. Math., 37 (1984), pp. 511-537. Zbl0598.60060MR745330
  16. [16] P.L. Lions - B. Perthame, Quasi variational inequalities and ergodic impulse control, SIAM J. Control Optim., 24, no. 4 (1986), pp. 604-615. MR846370
  17. [17] C. Miranda, Equazioni alle derivate parziali di tipo ellittico, Springer, Berlin, 1955. Zbl0065.08503MR87853
  18. [18] M.H. Protter - H.F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., 1967. Zbl0153.13602MR219861
  19. [19] M. Robin, On some impulse control problems with long run average cost, SIAM J. Control Optimiz., 19 (1981), pp. 333-358. Zbl0461.93062MR613099
  20. [20] M.H. Schaefer, Banach lattices and positive operators, Springer Verlag, Berlin-Heidelberg -New York, 1974. Zbl0296.47023MR423039
  21. [21] V.A. Solonnikov, On boundary value problems for linear general parabolic systems of differential equations, Trudy Mat. Inst. Steklov, Vol. 83 (1965). Zbl0164.12502MR211083
  22. [22] D. Stroock - S. Varadhan, Diffusion processes with boundary conditions, Comm. Pure Appl. Math., 24 (1971), pp. 147-225. Zbl0227.76131MR277037
  23. [23] G.M. Troianiello, Elliptic Differential Equations and Unilateral Problems, Plenum Publishing Co., to appear. MR1094820
  24. [24] G.M. Troianiello, On a class of unilateral evolution problems, Manuseripta Math., 29 (1979), pp. 353-384. Zbl0426.35050MR545049

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.