• 348 Citations
  • 13 h-Index
20032019
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Research Output 2003 2019

  • 348 Citations
  • 13 h-Index
  • 36 Article
  • 2 Comment/debate
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Article
2019

A note on boundary blow-up problem of ∆u = u p

Kim, S., 2019 Jan 1, In : Bulletin of the Korean Mathematical Society. 56, 1, p. 245-251 7 p.

Research output: Contribution to journalArticle

Boundary Blow-up
Blow-up Solution
Bounded Domain
Positive Solution
Uniqueness
1 Citation (Scopus)

Green’s function for second order elliptic equations with singular lower order coefficients

Kim, S. & Sakellaris, G., 2019 Mar 4, In : Communications in Partial Differential Equations. 44, 3, p. 228-270 43 p.

Research output: Contribution to journalArticle

Second Order Elliptic Equations
Green's function
Coefficient
Mathematical operators
Lorentz Spaces
2 Citations (Scopus)

Partial Schauder Estimates for Second-Order Elliptic and Parabolic Equations: A Revisit

Dong, H. & Kim, S., 2019 Apr, In : International Mathematics Research Notices. 2019, 7, p. 2085-2136 52 p.

Research output: Contribution to journalArticle

Schauder Estimates
Second Order Elliptic Equations
Parabolic Equation
Partial
Seminorm
2018
1 Citation (Scopus)

A Stable and Convergent Hodge Decomposition Method for Fluid–Solid Interaction

Yoon, G., Min, C. & Kim, S., 2018 Aug 1, In : Journal of Scientific Computing. 76, 2, p. 727-758 32 p.

Research output: Contribution to journalArticle

Fluid-solid Interaction
Hodge Decomposition
Decomposition Method
Poisson equation
Projection
2 Citations (Scopus)

Fundamental solutions for second-order parabolic systems with drift terms

Dong, H. & Kim, S., 2018 Jul, In : Proceedings of the American Mathematical Society. 146, 7, p. 3019-3029 11 p.

Research output: Contribution to journalArticle

Second-order Systems
Parabolic Systems
Fundamental Solution
Divergence-free
Coefficient

Green’s Function for Second Order Elliptic Equations in Non-divergence Form

Hwang, S. & Kim, S., 2018 Jan 1, (Accepted/In press) In : Potential Analysis.

Research output: Contribution to journalArticle

Second Order Elliptic Equations
Green's function
Oscillation
Derivative
Coefficient
6 Citations (Scopus)

On C1 , C2 , and weak type-(1, 1) estimates for linear elliptic operators: part II

Dong, H., Escauriaza, L. & Kim, S., 2018 Feb 1, In : Mathematische Annalen. 370, 1-2, p. 447-489 43 p.

Research output: Contribution to journalArticle

Elliptic Operator
Linear Operator
Elliptic Equations
Coefficient
Estimate

Uniqueness of solutions for Keller–Segel system of porous medium type coupled to fluid equations

Bae, H., Kang, K. & Kim, S., 2018 Apr 15, In : Journal of Differential Equations. 264, 8, p. 5360-5387 28 p.

Research output: Contribution to journalArticle

Viscosity Method
Stokes System
Vanishing Viscosity
Uniqueness of Solutions
Variable Coefficients
2017
6 Citations (Scopus)

On C1, C2, and weak type-(1,1) estimates for linear elliptic operators

Dong, H. & Kim, S., 2017 Mar 4, In : Communications in Partial Differential Equations. 42, 3, p. 417-435 19 p.

Research output: Contribution to journalArticle

Modulus of Continuity
Elliptic Operator
Linear Operator
Continuously differentiable
Estimate
2015

On an elliptic equation arising from photo-acoustic imaging in inhomogeneous media

Ammari, H., Dong, H., Kang, H. & Kim, S., 2015 Jan 1, In : International Mathematics Research Notices. 2015, 22, p. 12105-12113 9 p.

Research output: Contribution to journalArticle

Photoacoustic Imaging
Neumann Condition
Hölder Continuity
Dirichlet conditions
Inhomogeneous Media

Regularity of a degenerate parabolic equation appearing in Vecer’s unified pricing of Asian options

Dong, H. & Kim, S., 2015 Jan 1, In : Bulletin of the Korean Mathematical Society. 52, 3, p. 947-953 7 p.

Research output: Contribution to journalArticle

Asian Options
Degenerate Parabolic Equation
Pricing
Regularity
Classical Solution
8 Citations (Scopus)

The Green function for the mixed problem for the linear Stokes system in domains in the plane

Ott, K. A., Kim, S. & Brown, R. M., 2015 Mar 1, In : Mathematische Nachrichten. 288, 4, p. 452-464 13 p.

Research output: Contribution to journalArticle

Stokes System
Lipschitz Domains
Mixed Boundary Value Problem
Mixed Problem
Green's function
2014
4 Citations (Scopus)

Green's functions for elliptic and parabolic systems with Robin-type boundary conditions

Choi, J. & Kim, S., 2014 Nov 1, In : Journal of Functional Analysis. 267, 9, p. 3205-3261 57 p.

Research output: Contribution to journalArticle

Parabolic Systems
Elliptic Systems
Green's function
Boundary conditions
Weak Solution
2 Citations (Scopus)

Green's functions for parabolic systems of second order in time-varying domains

Dong, H. & Kim, S., 2014 Jul 1, In : Communications on Pure and Applied Analysis. 13, 4, p. 1407-1433 27 p.

Research output: Contribution to journalArticle

Parabolic Systems
Green's function
Time-varying
Weak Solution
Estimate
6 Citations (Scopus)

Harnack inequality for nondivergent parabolic operators on Riemannian manifolds

Kim, S., Kim, S. & Lee, K. A., 2014 Jan 1, In : Calculus of Variations and Partial Differential Equations. 49, 1-2, p. 669-706 38 p.

Research output: Contribution to journalArticle

Parabolic Operator
Harnack Inequality
Riemannian Manifold
Nonnegative Curvature
Nonnegative Solution

Heat kernel for the elliptic system of linear elasticity with boundary conditions

Taylor, J., Kim, S. & Brown, R., 2014 Oct 1, In : Journal of Differential Equations. 257, 7, p. 2485-2519 35 p.

Research output: Contribution to journalArticle

Linear Elasticity
Heat Kernel
Elliptic Systems
Elasticity
Mixed Problem
2013
8 Citations (Scopus)

Green's function for second order parabolic systems with Neumann boundary condition

Choi, J. & Kim, S., 2013 Apr 1, In : Journal of Differential Equations. 254, 7, p. 2834-2860 27 p.

Research output: Contribution to journalArticle

Second-order Systems
Parabolic Systems
Neumann Boundary Conditions
Green's function
Neumann function
14 Citations (Scopus)

Neumann functions for second order elliptic systems with measurable coefficients

Choi, J. & Kim, S., 2013 Oct 2, In : Transactions of the American Mathematical Society. 365, 12, p. 6283-6307 25 p.

Research output: Contribution to journalArticle

Neumann function
Second-order Systems
Elliptic Systems
Weak Solution
Coefficient
7 Citations (Scopus)

The Green Function for Elliptic Systems in Two Dimensions

Taylor, J. L., Kim, S. & Brown, R. M., 2013 Sep 1, In : Communications in Partial Differential Equations. 38, 9, p. 1574-1600 27 p.

Research output: Contribution to journalArticle

Elliptic Systems
Green's function
Two Dimensions
Boundary conditions
Fundamental Solution
2012
13 Citations (Scopus)

Global Estimates for Green's Matrix of Second Order Parabolic Systems with Application to Elliptic Systems in Two Dimensional Domains

Cho, S., Dong, H. & Kim, S., 2012 Feb 1, In : Potential Analysis. 36, 2, p. 339-372 34 p.

Research output: Contribution to journalArticle

Green's Matrix
Second-order Systems
Parabolic Systems
Elliptic Systems
Estimate
6 Citations (Scopus)

Sharp estimates for the Neumann functions and applications to quantitative photo-acoustic imaging in inhomogeneous media

Ammari, H., Kang, H. & Kim, S., 2012 Jul 1, In : Journal of Differential Equations. 253, 1, p. 41-72 32 p.

Research output: Contribution to journalArticle

Photoacoustic Imaging
Acoustic imaging
Neumann function
Inhomogeneous Media
Mathematical operators
2011
39 Citations (Scopus)

Analyticity of layer potentials and L2 solvability of boundary value problems for divergence form elliptic equations with complex L coefficients

Alfonseca, M. A., Auscher, P., Axelsson, A., Hofmann, S. & Kim, S., 2011 Mar 20, In : Advances in Mathematics. 226, 5, p. 4533-4606 74 p.

Research output: Contribution to journalArticle

Layer Potentials
Analyticity
Elliptic Equations
Solvability
Divergence
3 Citations (Scopus)

Elliptic systems with measurable coefficients of the type of Lamé system in three dimensions

Kang, K. & Kim, S., 2011 Nov 1, In : Journal of Differential Equations. 251, 9, p. 2466-2493 28 p.

Research output: Contribution to journalArticle

Elliptic Systems
Green's function
Three-dimension
Heat Kernel
Coefficient
14 Citations (Scopus)

Partial Schauder estimates for second-order elliptic and parabolic equations

Dong, H. & Kim, S., 2011 Jan 1, In : Calculus of Variations and Partial Differential Equations. 40, 3, p. 481-500 20 p.

Research output: Contribution to journalArticle

Schauder Estimates
Second Order Elliptic Equations
Seminorm
Parabolic Equation
Divergence
2010
1 Citation (Scopus)

Biases in the prime number race of function fields

Cha, B. & Kim, S., 2010 Apr 1, In : Journal of Number Theory. 130, 4, p. 1048-1055 8 p.

Research output: Contribution to journalArticle

Function Fields
Prime number
Polynomial ring
Number field
Galois field
17 Citations (Scopus)

Global pointwise estimates for Green's matrix of second order elliptic systems

Kang, K. & Kim, S., 2010 Dec 1, In : Journal of Differential Equations. 249, 11, p. 2643-2662 20 p.

Research output: Contribution to journalArticle

Green's Matrix
Pointwise Estimates
Second-order Systems
Elliptic Systems
Estimate
2009
26 Citations (Scopus)

Green's matrices of second order elliptic systems with measurable coefficients in two dimensional domains

Dong, H. & Kim, S., 2009 Jun 1, In : Transactions of the American Mathematical Society. 361, 6, p. 3303-3323 21 p.

Research output: Contribution to journalArticle

Green's Matrix
Second-order Systems
Elliptic Systems
Pointwise Estimates
Coefficient
6 Citations (Scopus)

On a degenerate parabolic equation arising in pricing of Asian options

Kim, S., 2009 Mar 1, In : Journal of Mathematical Analysis and Applications. 351, 1, p. 326-333 8 p.

Research output: Contribution to journalArticle

Asian Options
Degenerate Parabolic Equation
Generalized Solution
Pricing
Boundary conditions
2008
13 Citations (Scopus)
Gaussian Estimates
Second-order Systems
Parabolic Systems
Fundamental Solution
Heat Kernel
14 Citations (Scopus)

On the Green's matrices of strongly parabolic systems of second order

Cho, S., Dong, H. & Kim, S., 2008 Oct 22, In : Indiana University Mathematics Journal. 57, 4, p. 1633-1677 45 p.

Research output: Contribution to journalArticle

Green's Matrix
Parabolic Systems
Fundamental Matrix
Estimate
Divergence
17 Citations (Scopus)

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

Dong, H., Kim, S. & Safonov, M., 2008 Feb 1, 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
63 Citations (Scopus)

The Green function estimates for strongly elliptic systems of second order

Hofmann, S. & Kim, S., 2007 Oct 1, In : Manuscripta Mathematica. 124, 2, p. 139-172 34 p.

Research output: Contribution to journalArticle

Elliptic Systems
Green's function
Green's Matrix
Perturbation
Pointwise Estimates
2004
17 Citations (Scopus)

Gaussian estimates for fundamental solutions to certain parabolic systems

Hofmann, S. & Kim, S., 2004 Jan 1, In : Publicacions Matematiques. 48, 2, p. 481-496 16 p.

Research output: Contribution to journalArticle

Gaussian Estimates
Parabolic Systems
Fundamental Solution
Coefficient
Upper bound
13 Citations (Scopus)

Harnack inequality for nondivergent elliptic operators on Riemannian manifolds

Kim, S., 2004 Feb, In : Pacific Journal of Mathematics. 213, 2, p. 281-293 13 p.

Research output: Contribution to journalArticle

Harnack Inequality
Elliptic Operator
Riemannian Manifold
Nonnegative Curvature
Ricci Curvature
2 Citations (Scopus)

On the regularity of solutions to a parabolic system related to Maxwell's equations

Kang, K., Kim, S. & Minut, A., 2004 Nov 1, In : Journal of Mathematical Analysis and Applications. 299, 1, p. 89-99 11 p.

Research output: Contribution to journalArticle

Regularity of Solutions
Parabolic Systems
Maxwell equations
Maxwell's equations
Electromagnetic fields
2003
14 Citations (Scopus)

On the hölder continuity of solutions of a certain system related to Maxwell's equations

Kang, K. & Kim, S., 2003 Jan 1, In : SIAM Journal on Mathematical Analysis. 34, 1, p. 87-100 14 p.

Research output: Contribution to journalArticle

Curl
Maxwell equations
Maxwell's equations
Electromagnetic fields
Weak Solution