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Boundary estimates for the first-order derivatives of a solution to a nondivergent parabolic equation with composite right-hand side and coefficients of lower-order derivatives

Abstract

A linear parabolic equation with special singularities is studied. A priori boundary estimates are established for the maximum of the modulus of the gradient of a solution and for the Hölder constants as well. These estimates depend linearly on the functions appearing on the right-hand side of the equation. Bibliography: 7 titles.

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Additional information

Translated fromProblemy Matematicheskogo Analiza, No. 14, 1995, pp. 3–27.

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Apushkinskaya, D.E., Nazarov, A.I. Boundary estimates for the first-order derivatives of a solution to a nondivergent parabolic equation with composite right-hand side and coefficients of lower-order derivatives. J Math Sci 77, 3257–3276 (1995). https://doi.org/10.1007/BF02364860

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Keywords

  • Parabolic Equation
  • Boundary Estimate
  • Special Singularity
  • Linear Parabolic Equation
  • Nondivergent Parabolic Equation