Maximum principles for boundary-degenerate linear parabolic differential operators

Preprint English OPEN
Feehan, Paul M. N.;
(2013)
  • Subject: Primary 35B50, 35B51, 35K65, secondary 35D40, 35K85, 60J60 | Mathematics - Probability | Mathematics - Analysis of PDEs

We develop weak and strong maximum principles for boundary-degenerate, linear, parabolic, second-order partial differential operators, $Lu := -u_t-\tr(aD^2u)-\langle b, Du\rangle + cu$, with \emph{partial} Dirichlet boundary conditions. The coefficient, $a(t,x)$, is ass... View more
  • References (46)
    46 references, page 1 of 5

    [1] R. A. Adams, Sobolev spaces, Academic Press, Orlando, FL, 1975.

    [2] A. Bensoussan and J. L. Lions, Applications of variational inequalities in stochastic control, North-Holland, New York, 1982.

    [3] A. Ciomaga, On the strong maximum principle for second-order nonlinear parabolic integro-di erential equations, Adv. Di erential Equations 17 (2012), no. 7-8, 635{671, arXiv:1006.2607.

    [4] M. G. Crandall, H. Ishii, and P-L. Lions, User's guide to viscosity solutions of second order partial di erential equations, Bull. Amer. Math. Soc. (N.S.) 27 (1992), 1{67.

    [5] P. Daskalopoulos and P. M. N. Feehan, C1;1 regularity for degenerate elliptic obstacle problems in mathematical nance, arXiv:1206.0831.

    [6] , Existence, uniqueness, and global regularity for variational inequalities and obstacle problems for degenerate elliptic partial di erential operators in mathematical nance, arXiv:1109.1075.

    [7] P. Daskalopoulos and R. Hamilton, C1-regularity of the free boundary for the porous medium equation, J. Amer. Math. Soc. 11 (1998), 899{965.

    [8] P. Daskalopoulos and E. Rhee, Free-boundary regularity for generalized porous medium equations, Commun. Pure Appl. Anal. 2 (2003), 481{494.

    [9] D. J. Du y, Finite di erence methods in nancial engineering, Wiley, New York, 2006.

    [10] E. Ekstrom and J. Tysk, Boundary conditions for the single-factor term structure equation, Ann. Appl. Probab. 21 (2011), 332{350.

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