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: Lewy example in PDE | Statement: [Hans Lewy, theoremNamedAfter, Lewy example in PDE]

Target entity: Lewy example in PDE
Context triple: [Hans Lewy, theoremNamedAfter, Lewy example in PDE]

• A. 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.
• B. Lectures on Partial Differential Equations
  "Lectures on Partial Differential Equations" is a concise, influential textbook by Vladimir Arnold that presents the theory of partial differential equations with a strong geometric and intuitive emphasis.
• C. Monge–Ampère equation
  The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
• 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. PDE
  PDE is the state agency responsible for overseeing public education and related policies in Pennsylvania.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: Lewy example in PDE
Triple: [Hans Lewy, theoremNamedAfter, Lewy example in PDE]

The Lewy example in PDE is a classical counterexample in the theory of partial differential equations that demonstrates the existence of a smooth linear PDE with no local solution, highlighting limitations of earlier existence theorems.

Target entity: Lewy example in PDE
Target entity description: The Lewy example in PDE is a classical counterexample in the theory of partial differential equations that demonstrates the existence of a smooth linear PDE with no local solution, highlighting limitations of earlier existence theorems.

• A. 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.
• B. Lectures on Partial Differential Equations
  "Lectures on Partial Differential Equations" is a concise, influential textbook by Vladimir Arnold that presents the theory of partial differential equations with a strong geometric and intuitive emphasis.
• C. Monge–Ampère equation
  The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
• 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. PDE
  PDE is the state agency responsible for overseeing public education and related policies in Pennsylvania.
• F. None of above. chosen