TY - JOUR
T1 - Schauder a priori estimates and regularity of solutions to boundary-degenerate elliptic linear second-order partial differential equations
AU - Feehan, Paul M.N.
AU - Pop, Camelia A.
PY - 2014/2/1
Y1 - 2014/2/1
N2 - We establish Schauder a priori estimates and regularity for solutions to a class of boundary-degenerate elliptic linear second-order partial differential equations. Furthermore, given a C∞-smooth source function, we prove C∞-regularity of solutions up to the portion of the boundary where the operator is degenerate. Boundary-degenerate elliptic operators of the kind described in our article appear in a diverse range of applications, including as generators of affine diffusion processes employed in stochastic volatility models in mathematical finance [10,25], generators of diffusion processes arising in mathematical biology [3,11], and the study of porous media [7,8].
AB - We establish Schauder a priori estimates and regularity for solutions to a class of boundary-degenerate elliptic linear second-order partial differential equations. Furthermore, given a C∞-smooth source function, we prove C∞-regularity of solutions up to the portion of the boundary where the operator is degenerate. Boundary-degenerate elliptic operators of the kind described in our article appear in a diverse range of applications, including as generators of affine diffusion processes employed in stochastic volatility models in mathematical finance [10,25], generators of diffusion processes arising in mathematical biology [3,11], and the study of porous media [7,8].
KW - A priori Schauder estimate
KW - Boundary-degenerate elliptic partial differential operator
KW - Degenerate diffusion process
KW - Hölder regularity
KW - Mathematical finance
KW - Primary
KW - Secondary
UR - http://www.scopus.com/inward/record.url?scp=84888010660&partnerID=8YFLogxK
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U2 - 10.1016/j.jde.2013.08.012
DO - 10.1016/j.jde.2013.08.012
M3 - Article
AN - SCOPUS:84888010660
SN - 0022-0396
VL - 256
SP - 895
EP - 956
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 3
ER -