## Boundary value problems of mathematical physics and related aspects of function theory, Part 1 |

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### Contents

Global Solvability of the First Boundary Value Problem for a Quasilinear Parabolic Equation | 1 |

Nonlocal Estimates of First Derivatives of Solutions to Dirichlets Problem | 12 |

One Class of Functions of Many Real Variables u Q n u Q u Q Q | 35 |

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Akad analogous arbitrary assertion assume bilinear form boundary problem Boundary Value Problems Cauchy inequality Cauchy problem Chapter characteristic function classes of functions coefficients consider constant continuously differentiable function cylinder QT defined denote depending derivatives of solutions Dirichlet problem Dokl double operator integrals Equa Equations 100 exists finite following equation Formula Hilbert space Holder inequality Inequality 21 inequality cf inequality is valid Inst interval Ladyzhenskaya and N. N. Lemma let Q Linear and Quasilinear maximum modulus measurable space N. N. Ural'tseva Nauk SSSR Navier—Stokes equations nonnegative nonuniformly elliptic equations norm notation O. A. Ladyzhenskaya obtain the following paper parabolic equations polynomial prion priori estimates proof of Theorem properties proven quasilinear equations region Q result right side Russian satisfies Condition satisfying the conditions solvability space spectral measure Steklov Mathematical Institute surface theory tion transformer variables vector Volterra operators