Mathematics Branches, Topics, and Sub-Topics

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35Dxx Generalized solutions

This subtopic studies generalized solutions of PDEs, where weak, distributional, or variational formulations extend classical solution concepts.

Specific topics

35D30 Weak solutions to PDEs

Overview

35D30 studies weak solutions to pdes in generalized solutions of PDE. It studies weak, distributional, and variational notions of solution when classical derivatives are unavailable.

Related Wikipedia Page

Generalized Solutions Of Pde (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for weak solutions to pdes
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to make PDE solvable in low-regularity contexts and to develop variational methods.

Applications

  • Weak formulations
  • Distributions and Sobolev spaces
  • Variational PDE methods

References

Recommended Textbooks

35D35 Strong solutions to PDEs

Overview

35D35 studies strong solutions to pdes in generalized solutions of PDE. It studies weak, distributional, and variational notions of solution when classical derivatives are unavailable.

Related Wikipedia Page

Generalized Solutions Of Pde (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for strong solutions to pdes
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to make PDE solvable in low-regularity contexts and to develop variational methods.

Applications

  • Weak formulations
  • Distributions and Sobolev spaces
  • Variational PDE methods

References

Recommended Textbooks

35D40 Viscosity solutions to PDEs

Overview

35D40 studies viscosity solutions to pdes in generalized solutions of PDE. It studies weak, distributional, and variational notions of solution when classical derivatives are unavailable.

Related Wikipedia Page

Generalized Solutions Of Pde (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for viscosity solutions to pdes
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to make PDE solvable in low-regularity contexts and to develop variational methods.

Applications

  • Weak formulations
  • Distributions and Sobolev spaces
  • Variational PDE methods

References

Recommended Textbooks