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Note on local estimates for weak solution of boundary value problem for second order parabolic equation
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The aim of this note is to provide detailed proofs for local estimates near the boundary for weak solutions of second order parabolic equations in divergence form with time-dependent measurable coefficients subject to Neumann boundary condition. The corresponding parabolic equations with Dirichlet boundary condition are also considered.
Abstract
The aim of this note is to provide detailed proofs for local estimates near the boundary for weak solutions of second order parabolic equations in divergence form with time-dependent measurable coefficients subject to Neumann boundary condition. The corresponding parabolic equations with Dirichlet boundary condition are also considered.
참고문헌 (8)
- J. Choi, "Green’s function for second order parabolic systems with Neumann boundary condition", J. Differential Equations, 254(7), pp.2834~2860 (2013)
- M. Choulli, "Local boundedness property for parabolic BVP’s and the Gaussian upper bound for their Green functions", Evol. Equ. Control Theory, 4(1), pp.61~67 (2015)
- E. DiBenedetto, "Partial Differential Equations" (2010), Birkhauser Boston, Inc.
- D. Gilbarg, "Elliptic Partial Differential Equations of Second Order" (2001), Springer-Verlag
- 김세익, "NOTE ON LOCAL BOUNDEDNESS FOR WEAK SOLUTIONS OF NEUMANN PROBLEM FOR SECOND-ORDER ELLIPTIC EQUATIONS", Journal of the Korean Society for Industrial and Applied Mathematics, 19(2), pp.189~195 (2015), 한국산업응용수학회[DOI]
- O. A. Ladyzhenskaya, "Linear and Quasilinear Equations of Parabolic Type" (1967), American Mathematical Society
- G. M. Lieberman, "Second Order Parabolic Differential Equations" (1996), World Scientific Publishing Co., Inc.
- L. G. Rogers, "Degree-independent Sobolev extension on locally uniform domains", J. Funct. Anal, 235(2), pp.619~665 (2006)
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