Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How to solve smooth nonlinear PDEs in algebras of generalized functions
  with dense singularities   As a significant strengthening of properties of earlier algebras of
generalized functions, here are presented classes of such algebras which can
deal with dense singularities. In fact, the cardinal of the set of singular
points can be larger than that of the nonsingular points. This large class of
singularities allows the solution of large classes of smooth nonlinear PDEs.
This in certain ways overcomes the celebrated 1957 H. Lewy impossibility
result.

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The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci