mathematics

Michael Struwe

Michael Struwe is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Michael Struwe rather than just read about it. In short: Michael Struwe (born 6 October 1955 in Wuppertal) is a German mathematician who specializes in calculus of variations and nonlinear partial differential equations. He won the 2012 Cantor medal from the Deutsche Mathematiker-Vereinigung for "outstanding achievements in the field of geometric analysis, calculus of variations and nonlinear partial differential equations".

Key takeaways

Michael Struwe belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Michael Struwe to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Michael Struwe from memory before moving on to harder problems.

Reference excerpt

Michael Struwe (born 6 October 1955 in Wuppertal) is a German mathematician who specializes in calculus of variations and nonlinear partial differential equations. He won the 2012 Cantor medal from the Deutsche Mathematiker-Vereinigung for "outstanding achievements in the field of geometric analysis, calculus of variations and nonlinear partial differential equations". He studied mathematics at the University of Bonn, gaining his PhD in 1980 with the title Infinitely Many Solutions for Superlinear, Anticoercive Elliptic Boundary Value Problems without Oddness. He took research positions in Paris and at ETH Zürich before gaining his habilitation in Bonn in 1984. Since 1986, he has been working at ETH Zürich, initially as an assistant professor, becoming a full professor in 1993. His specialisms included nonlinear partial differential equations and calculus of variations. He is joint editor of the journals Calculus of Variations, Commentarii Mathematici Helvetici, International Mathematical Research Notices and Mathematische Zeitschrift. His publications include the book Variational methods (Applications to nonlinear PDE and Hamiltonian systems) (Springer-Verlag, 1990), which was praised by Jürgen Jost as "very useful" with an "impressive range of often difficult examples". Struwe was awarded a Gauss Lecture by the German Mathematical Society in 2011. In 2012, Struwe was selected as one of the inaugural fellows of the American Mathematical Society.

Major publications Giaquinta, Mariano; Struwe, Michael (1982). "On the partial regularity of weak solutions of nonlinear parabolic systems". Mathematische Zeitschrift. 179 (4). Springer Science and Business Media LLC: 437–451. doi:10.1007/bf01215058. ISSN 0025-5874. S2CID 121187999. Struwe, Michael (1984). "A global compactness result for elliptic boundary value problems involving limiting nonlinearities". Mathematische Zeitschrift. 187 (4). Springer Science and Business Media LLC: 511–517. doi:10.1007/bf01174186. ISSN 0025-5874. S2CID 120970687. Struwe, Michael (1985). "On the evolution of harmonic mappings of Riemannian surfaces". Commentarii Mathematici Helvetici. 60 (1). European Mathematical Society - EMS - Publishing House GmbH: 558–581. doi:10.1007/bf02567432. ISSN 0010-2571. S2CID 122295509. Cerami, G; Solimini, S; Struwe, M (1986). "Some existence results for superlinear elliptic boundary value problems involving critical exponents". Journal of Functional Analysis. 69 (3). Elsevier BV: 289–306. doi:10.1016/0022-1236(86)90094-7. ISSN 0022-1236. Struwe, Michael (1988). "On partial regularity results for the navier-stokes equations". Communications on Pure and Applied Mathematics. 41 (4). Wiley: 437–458. doi:10.1002/cpa.3160410404. ISSN 0010-3640. Struwe, Michael (1988). "The existence of surfaces of constant mean curvature with free boundaries". Acta Mathematica. 160. International Press of Boston: 19–64. doi:10.1007/bf02392272. ISSN 0001-5962. S2CID 121385750. Struwe, Michael. On the evolution of harmonic maps in higher dimensions. J. Differential Geom. 28 (1988), no. 3, 485–502. Chen, Yunmei; Struwe, Michael (1989). "Existence and partial regularity results for the heat flow for harmonic maps". Mathematische Zeitschrift. 201 (1). Springer Science and Business Media LLC: 83–103. doi:10.1007/bf01161997. ISSN 0025-5874. S2CID 11210055. Shatah, Jalal; Struwe, Michael (1993). "Regularity Results for Nonlinear Wave Equations". The Annals of Mathematics. 138 (3). JSTOR: 503. doi:10.2307/2946554. ISSN 0003-486X. JSTOR 2946554. Shatah, Jalal; Struwe, Michael (1994). "Well-posedness in the energy space for semilinear wave equations with critical growth". International Mathematics Research Notices. 1994 (7). Oxford University Press (OUP): 303. doi:10.1155/s1073792894000346. ISSN 1073-7928. Struwe, Michael; Tarantello, Gabriella. On multivortex solutions in Chern-Simons gauge theory. Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 1 (1998), no. 1, 109–121.

References

External links page at ETH

Illustrations

Worked examples

Example 1 — a first encounter with Michael Struwe

Start with the simplest possible case. Write down what Michael Struwe claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Michael Struwe before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Michael Struwe ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Michael Struwe

In research: Michael Struwe appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Michael Struwe in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Michael Struwe is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1955 births, 20th-century German mathematicians, 21st-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Michael Struwe outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Michael Struwe in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Michael Struwe means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Michael Struwe out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Michael Struwe in simple terms?

Why does Michael Struwe matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Michael Struwe?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Michael Struwe.