| Preface | |
| Two-sided estimates for polynomials related to Newton's polygon and their application to studying local properties of partial differential operators in two variables | p. 1 |
| Newton's polygon of a polynomial in two variables | p. 2 |
| Polynomials admitting of two-sided estimates | p. 13 |
| N Quasi-elliptic polynomials in two variables | p. 22 |
| N Quasi-elliptic differential operators | p. 27 |
| Parabolic operators associated with Newton's polygon | p. 49 |
| Polynomials correct in Petrovskii's sense | p. 50 |
| Two-sided estimates for polynomials in two variables satisfying Petrovskii's condition. N-parabolic polynomials | p. 57 |
| Cauchy's problem for N-stable correct and N-parabolic differential operators in the case of one spatial variable | p. 64 |
| Stable-correct and parabolic polynomials in several variables | p. 75 |
| Cauchy's problem for stable-correct differential operators with variable coefficients | p. 81 |
| Dominantly correct operators | p. 93 |
| Strictly hyperbolic operators | p. 94 |
| Dominantly correct polynomials in two variables | p. 97 |
| Dominantly correct differential operators with variable coefficients (the case of two variables) | p. 104 |
| Dominantly correct polynomials and the corresponding differential operators (the case of several spatial variables) | p. 111 |
| Operators of principal type associated with Newton's polygon | p. 118 |
| Introduction. Operators of principal and quasi-principal type | p. 118 |
| Polynomials of N-principal type | p. 124 |
| The main L[subscript 2] estimate for operators of N-principal type | p. 135 |
| Local solvability of differential operators of N-principal type | p. 150 |
| Two-sided estimates in several variables relating to Newton's polyhedra | p. 158 |
| Estimates for polynomials in R[superscript n] relating to Newton's polyhedra | p. 158 |
| Two-sided estimates in some regions in R[superscript n] relating to Newton's polyhedron. Special classes of polynomials and differential operators in several variables | p. 169 |
| Operators of principal type associated with Newton's polyhedron | p. 177 |
| Polynomials of N-principal type | p. 177 |
| Estimates for polynomials of N-principal type in regions of special form | p. 186 |
| The covering of R[superscript n] by special regions associated with Newton's polyhedron | p. 193 |
| Differential operators of N-principal type with variable coefficients | p. 200 |
| The method of energy estimates in Cauchy's problem | p. 215 |
| Introduction. The functional scheme of the proof of the solvability of Cauchy's problem | p. 215 |
| Sufficient conditions for the existence of energy estimates | p. 223 |
| An analysis of conditions for the existence of energy estimates | p. 235 |
| Cauchy's problem for dominantly correct differential operators | p. 247 |
| References | p. 261 |
| Index | p. 265 |
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