## Boundary value problems of mathematical physics and related aspects of function theory, Part 2 |

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### Contents

Estimates of Convolution Operators | 1 |

Local Maximal Estimates of the Modulus of the First Derivatives of the Solutions | 37 |

Modifications of the NavierStokes Equations for Large Velocity Gradients | 57 |

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Akad analogous arbitrary assume ball boundary boundary-value problem bounded function boundedness Cauchy inequality Cauchy problem Chapt class of functions coefficients components condition 0.2 convergence convolution operator cutoff function deduce denote derivatives differential equations Dirichlet problem domain Q elliptic equations equal to zero estimated in terms finite ﬂu following inequality holds following theorem Fourier series Fourier transform func Function Theory Holder Holder inequality Inasmuch inequalities 2.9 Inst integral identity investigate K. K. Golovkin kernel left-hand side Lemma linear set matrix Moscow multi-index Nauk SSSR Navier-Stokes equations O. A. Ladyzhenskaya obtain operator 54 ordinary differential equations parabolic equations Problems of Mathematical properties proved the following quasilinear right-hand side satisfies condition satisfying the condition smoothness solution of problem space Steklov Mathematical Institute subdomain sufficiently large tion Trudy Mat unique solvability V. A. Solonnikov valid variables verified virtue