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The 16 pages that link to Maximum principle, each with the reason it gives.

• Boundary conditionsRelated: It shows how boundary values can control an entire solution.

• Boundary value problemRelated: It can establish uniqueness and bounds from boundary data for elliptic problems.

• Heat equationRelated: It rules out new interior temperature maxima or minima during diffusion.

• Poisson's equationRelated: It constrains Poisson solutions when the source and boundary values are known.

• Laplace's equationRelated: It explains why boundary data control extrema of harmonic solutions.

• Elliptic partial differential equationRelated: It gives uniqueness and qualitative bounds for many elliptic boundary-value problems.

• Maximum modulus principleNarrower topic: The maximum modulus principle is the complex-analytic member of this broader family.

• Harmonic functionRelated: It rules out strict interior maxima and minima for nonconstant harmonic functions.

• Dirichlet boundary conditionRelated: For harmonic functions, boundary values bound the solution throughout the domain.

• Dirichlet problemRelated: It often proves that a harmonic Dirichlet solution is unique.

• Geometric analysisRelated: It yields estimates that control solutions to geometric evolution and elliptic equations.

• Parabolic partial differential equationRelated: It captures how parabolic evolution prevents new interior maxima under suitable conditions.

• Earnshaw's theoremRelated: It gives a mathematical route from Laplace’s equation to the absence of stable potential wells.

• Phragmén–Lindelöf principleNarrower topic: This broader principle supplies the common framework behind the unbounded-domain extension.

• Harnack's principleRelated: It underlies rigidity properties that complement the bounds used in Harnack's argument.

• Weyl's lemmaRelated: Once smoothness is established, classical harmonic-function principles apply to the representative.