Mikhail V Safonov

1977 …2020
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Research Output 1977 2018

2018

On the boundary estimates for second-order elliptic equations

Safonov, M. V., Aug 3 2018, In : Complex Variables and Elliptic Equations. 63, 7-8, p. 1123-1141 19 p.

Research output: Contribution to journalArticle

Second Order Elliptic Equations
Elliptic Equations
Estimate
Nonexistence
Form
2017

On second order elliptic and parabolic equations of mixed type

Chen, G. & Safonov, M. V., Apr 15 2017, In : Journal of Functional Analysis. 272, 8, p. 3216-3237 22 p.

Research output: Contribution to journalArticle

Harnack Inequality
Second Order Elliptic Equations
Elliptic Equations
Parabolic Equation
Strictly positive
2016

Narrow domains and the harnack inequality for elliptic equations

Safonov, M. V., Jan 1 2016, In : St. Petersburg Mathematical Journal. 27, 3, p. 509-522 14 p.

Research output: Contribution to journalArticle

Harnack Inequality
Elliptic Equations
Estimate
Iteration
2011
2 Citations (Scopus)

Boundary Harnack principle for second order elliptic equations with unbounded drift

Kim, H. & Safonov, M. V., Nov 1 2011, In : Journal of Mathematical Sciences. 179, 1, p. 127-143 17 p.

Research output: Contribution to journalArticle

Boundary Harnack Principle
Second Order Elliptic Equations
Bibliographies
Bounded Domain
Regularity
3 Citations (Scopus)

Carleson type estimates for second order elliptic equations with unbounded drift

Kim, H. & Safonov, M. V., Aug 1 2011, In : Journal of Mathematical Sciences. 176, 6, p. 928-944 17 p.

Research output: Contribution to journalArticle

Second Order Elliptic Equations
Bibliographies
Regularity Conditions
Positive Solution
Bounded Domain
2008
16 Citations (Scopus)

On uniqueness of boundary blow-up solutions of a class of nonlinear elliptic equations

Dong, H., Kim, S. & Safonov, M. V., Feb 1 2008, In : Communications in Partial Differential Equations. 33, 2, p. 177-188 12 p.

Research output: Contribution to journalArticle

Boundary Blow-up
Blow-up Solution
Nonlinear Elliptic Equations
Semilinear Elliptic Equations
Uniqueness Theorem
2007
17 Citations (Scopus)
Harnack Inequality
Parabolic Equation
Positive Solution
Linear equation
Bundle
1 Citation (Scopus)

Harnack's estimates: Positivity and local behavior of degenerate and singular parabolic equations

DiBenedetto, E., Gianazza, U., Safonov, M. V., Urbano, J. M. & Vespri, V., Apr 27 2007, In : Boundary Value Problems. 2007, 42548.

Research output: Contribution to journalEditorial

Singular Equation
Positivity
Parabolic Equation
Estimate
1999
41 Citations (Scopus)

Behavior near the boundary of positive solutions of second order parabolic equations. II

Fabes, E. B., Safonov, M. V. & Yuan, Y. U., Dec 1 1999, In : Transactions of the American Mathematical Society. 351, 12, p. 4947-4961 15 p.

Research output: Contribution to journalArticle

Second Order Equations
Parabolic Equation
Positive Solution
Harnack Inequality
Lipschitz Domains
21 Citations (Scopus)

Doubling properties for second order parabolic equations

Safonov, M. V. & Yuan, Y., Jan 1 1999, In : Annals of Mathematics. 150, 1, p. 313-327 15 p.

Research output: Contribution to journalArticle

Harnack Inequality
Doubling
Second Order Equations
Parabolic Equation
Green's function
35 Citations (Scopus)

Nonuniqueness for second-order elliptic equations with measurable coefficients

Safonov, M. V., Jan 1 1999, In : SIAM Journal on Mathematical Analysis. 30, 4, p. 879-895 17 p.

Research output: Contribution to journalArticle

Second Order Elliptic Equations
Nonuniqueness
Elliptic Operator
Dirichlet Problem
Weak Solution
1997
27 Citations (Scopus)

Behavior Near the Boundary of Positive Solutions of Second Order Parabolic Equations

Fabes, E. B. & Safonov, M. V., Dec 1 1997, In : Journal of Fourier Analysis and Applications. 3, SPEC. ISS.

Research output: Contribution to journalArticle

Second Order Equations
Parabolic Equation
Positive Solution
1995
6 Citations (Scopus)

On the Oblique Derivative Problem for Second Order Elliptic Equations

Safonov, M. V., Jan 1 1995, In : Communications in Partial Differential Equations. 20, 7-8, p. 1349-1367 19 p.

Research output: Contribution to journalArticle

Second Order Elliptic Equations
Oblique
Derivatives
Derivative
26 Citations (Scopus)

The abstract cauchy‐kovalevskaya theorem in a weighted banach space

Safonov, M. V., Jan 1 1995, In : Communications on Pure and Applied Mathematics. 48, 6, p. 629-637 9 p.

Research output: Contribution to journalArticle

Banach spaces
Banach space
Theorem
Nonlinear Problem
Cauchy Problem
1994
12 Citations (Scopus)

On a weak uniqueness for some elliptic equations

Safonov, M. V., Jan 1 1994, In : Communications in Partial Differential Equations. 19, 5-6, p. 943-957 15 p.

Research output: Contribution to journalArticle

Hausdorff Measure
Second derivative
Closed set
Elliptic Equations
Uniqueness
1989
20 Citations (Scopus)

On the classical solution of nonlinear elliptic equations of second order

Safonov, M. V., Jun 30 1989, In : Mathematics of the USSR - Izvestija. 33, 3, p. 597-612 16 p.

Research output: Contribution to journalArticle

Bellman Equation
Nonlinear Elliptic Equations
Classical Solution
Dirichlet Problem
Coefficient
1988
14 Citations (Scopus)
Elliptic Equations
Linear equation
Coefficient
Estimate
Hölder Space
1987
Hamilton-Jacobi-Bellman Equation
Degeneracy
Nonlinearity
Coefficient
2 Citations (Scopus)

Smoothness near the boundary of the solutions of the elliptic Bellman equations

Safonov, M. V., Apr 1 1987, In : Journal of Soviet Mathematics. 37, 1, p. 885-888 4 p.

Research output: Contribution to journalArticle

Bellman Equation
Elliptic Equations
Smoothness
Derivatives
Second derivative
1983
34 Citations (Scopus)

Harnack's inequality for elliptic equations and the Hölder property of their solutions

Safonov, M. V., Mar 1 1983, In : Journal of Soviet Mathematics. 21, 5, p. 851-863 13 p.

Research output: Contribution to journalArticle

Harnack Inequality
Elliptic Equations
Derivatives
Second Order Elliptic Equations
Second-order Derivatives
1981
118 Citations (Scopus)

A certain property of solutions of parabolic equations with measurable coefficients

Krylov, N. V. & Safonov, M. V., Feb 28 1981, In : Mathematics of the USSR - Izvestija. 16, 1, p. 151-164 14 p.

Research output: Contribution to journalArticle

Parabolic Equation
Hölder Exponent
Harnack Inequality
Coefficient
Second derivative
1978
3 Citations (Scopus)

On the dirichlet problem for bellman's equation in a plane domain. II

Safonov, M. V., Apr 30 1978, In : Mathematics of the USSR - Sbornik. 34, 4, p. 521-526 6 p.

Research output: Contribution to journalArticle

Bellman Equation
Nondegeneracy
Dirichlet Problem
Smoothness
Generalized Solution
1977
4 Citations (Scopus)

On The Dirichlet Problem for Bellman’s Equation in A Plane Domain

Safonov, M. V., Feb 28 1977, In : Mathematics of the USSR - Sbornik. 31, 2, p. 231-248 18 p.

Research output: Contribution to journalArticle

Bellman Equation
Dirichlet Problem
Smoothness
Controlled Diffusions
Nondegeneracy