Publications (3)0 Total impact
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Article: Rate of convergence of finite-difference approximations for degenerate linear parabolic equations with $C^1$ and $C^2$ coefficients
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ABSTRACT: We consider degenerate parabolic and elliptic equations of second order with $C^1$ and $C^2$ coefficients. Error bounds for certain types of finite-difference schemes are obtained.Electronic Journal of Differential Equations. 01/2005; -
Article: On Regularity Of Transition Probabilities And Invariant Measures Of Singular Diffusions Under Minimal Conditions
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ABSTRACT: . Let A = (a ij ) be a matrix-valued Borel mapping on a domain# # R d , let b = (b i ) be a vector field on # and let L A,b # = a ij # x i # x j # + b i # x i #. We study Borel measures on# that satisfy the elliptic equation L # A,b = 0 in the weak sense: # L A,b # d = 0 for all # # C # 0(#2 We prove that, under mild conditions, has a density. If A is locally uniformly nondegenerate, A # H p,1 loc and b # L p loc for some p > d, then this density belongs to H p,1 loc . Actually, we prove Sobolev regularity for solutions of certain generalized nonlinear elliptic inequalities. Analogous results are obtained in the parabolic case. These results are applied to transition probabilities and invariant measures of di#usion processes. AMS 1991 Subject classification: Primary: 35J15, 35K10, 60J35 Secondary: 35D10, 35B65, 60J60, 35R05 Keywords and phrases: elliptic regularity, parabolic regularity, invariant measure, sub-Markovian semigroup, singular di#usion, Runn...01/2000; -
Article: Elliptic regularity and essential self-adjointness of Dirichlet operators on
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ABSTRACT: We prove a new regularity result for operators of type L = Delta +BDeltar+c, on open setsOmega ae IR n , provided B :Omega ! IR n , c :Omega ! IR satisfy mild integrability conditions. As a consequence we prove that L = Delta + r log ae Delta r with domain C 1 0 (IR n ) is essentially self-adjoint on L 2 (IR n ; aedx), if ae 2 H 1;1 loc (IR n ) and r log ae 2 L fl loc (IR n ; dx) for some fl ? n. AMS Subject Classification Primary: 47 B 25, 35 B 65 Secondary: 31 C 25 Key words and phrases: Dirichlet operators, generalized Schrodinger operators, regularity of weak solutions, essential self-adjointness Running head: Dirichlet operators on IR n 1) Department of Mechanics and Mathematics, Moscow State University, 119899 Moscow, Russia 2) School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA 3) Fakultat fur Mathematik, Universitat Bielefeld, D--33501 Bielefeld, Germany 1 One of the classical problems in mathematical physics is th...05/1999;
