Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Hadamard’s definition of well-posedness | Statement: [Hadamard’s example of ill-posed problems, relatedTo, Hadamard’s definition of well-posedness]

Target entity: Hadamard’s definition of well-posedness
Context triple: [Hadamard’s example of ill-posed problems, relatedTo, Hadamard’s definition of well-posedness]

• A. Hadamard’s example of ill-posed problems chosen
  Hadamard’s example of ill-posed problems is a classical mathematical construction illustrating how small changes in input data can cause large, unstable changes in solutions, thereby violating the standard criteria for well-posedness in analysis and partial differential equations.
• B. Hilbert’s nineteenth problem
  Hilbert’s nineteenth problem is one of David Hilbert’s famous list of 23 problems, asking whether solutions to regular variational problems are always analytic.
• C. Agmon–Douglis–Nirenberg estimates
  Agmon–Douglis–Nirenberg estimates are fundamental a priori estimates in the theory of linear elliptic partial differential equations and systems, providing precise control of solution regularity in terms of data norms.
• D. Lectures on Cauchy’s problem in linear partial differential equations
  "Lectures on Cauchy’s Problem in Linear Partial Differential Equations" is a classic mathematical treatise by Jacques Hadamard that systematically develops the theory of existence, uniqueness, and well-posedness for solutions to linear partial differential equations.
• E. Hilbert’s twenty-second problem
  Hilbert’s twenty-second problem is one of David Hilbert’s famous list of 23 problems, concerning the uniformization of analytic relations and the representation of multi-valued analytic functions by single-valued ones on suitable Riemann surfaces.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.