This quantity develops the tactic of Newton's polyhedron for fixing a few difficulties within the thought of partial differential equations. The content material is split into components. Chapters 1-4 think of Newton's polygon and Chapters 5-7 give some thought to Newton's polyhedron. The case of the polygon makes it attainable not just to contemplate basic buildings within the two-dimensional case, but in addition ends up in a few usual multidimensional purposes. realization is principally interested in a targeted category of hypoelliptic operators outlined utilizing Newton's polyhedron, power estimates in Cauchy's challenge in terms of Newton's polyhedron, and generalized operators of valuable style. precedence is given to the presentation of an algebraic approach that are utilized to many different difficulties to boot. For researchers and graduate scholars whose paintings contains the idea of differential and pseudodifferential equations.
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