2016
DOI: 10.1016/j.jmaa.2016.03.056
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A model of solvable second order PDE with non-smooth coefficients

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Cited by 7 publications
(9 citation statements)
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“…These classes, analyzed by the author in [5], represent a variation with non-smooth coefficients of the class (1.1). Here the local solvability problem is considered only at points of S (unlike the smooth case), since, far from S, these classes are contained in the main class (1.1) and the results true for (1.1) apply.…”
Section: Introductionmentioning
confidence: 99%
“…These classes, analyzed by the author in [5], represent a variation with non-smooth coefficients of the class (1.1). Here the local solvability problem is considered only at points of S (unlike the smooth case), since, far from S, these classes are contained in the main class (1.1) and the results true for (1.1) apply.…”
Section: Introductionmentioning
confidence: 99%
“…We give here the sketch of the proof by listing the main steps (see [4] for the details). Recall that the goal is to obtain the solvability estimate from which the result follows.…”
Section: Sketch Of the Proofmentioning
confidence: 99%
“…Step First, given a point x 0 ∈ S and λ ∈ R (that will be chosen in the next step), we prove that there exists a compact set K 0 ⊂ (containing x 0 in its interior) such that the quantity 2Re(P * 2 ϕ, e 2λf ϕ) can be estimated from below as follows (see [4]):…”
Section: Firstmentioning
confidence: 99%
See 1 more Smart Citation
“…Our main motivation in studying such a class of degenerate differential operators is to push the frontier for the solvability in presence of multiple characteristics. Besides the papers [1], [4], [9] and [8] (in which a case with non-smooth coefficients is studied), and the book [13] (where one can find an updated account of the solvability issue under the (Ψ) condition of Nirenberg and Treves, problem solved by Dencker in [5]), we wish to recall a number of works related to the local solvability of operators with multiple characteristics, such as [21], [16,17], [14], [23,25], [20], [15], [12], [18], and [6,7] (see also [19] and references therein). In particular, among them we wish to single out the recent paper [7] by Dencker in which he introduces the class of sub-principal type operators (whose characteristics are involutive) for which he gave necessary conditions for local solvability, and the paper [18] by Parenti and Parmeggiani (see also [19]) in which they obtain semiglobal solvability results (with a loss of many derivatives) for operators with transversal multiple symplectic characteristics.…”
Section: Introductionmentioning
confidence: 99%