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Everything about Dirichlet problem
Problem of solving a partial differential equation subject to prescribed boundary values
In mathematics, a Dirichlet problem asks for a function which solves a specified partial differential equation (PDE) in the interior of a given region that takes prescribed values on the boundary of the region. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Dirichlet problemA 5-minute orientation
- Skim a recent paper: Nehari manifold and fractional Dirichlet boundary value problemInfluential work since 2022
- Pick up a classic book: On Dirichlet's boundary value problemThe most-reprinted book on the subject
- Read the landmark paper: On a singular nonlinear dirichlet problemCited 202 times
- Go sideways: Fokas methodA closely related topic
- Go sideways: Stochastic processes and boundary value problemsA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
On a singular nonlinear dirichlet problem
The Dirichlet Problem
The Dirichlet problem for nonlocal operators
The Dirichlet Casimir problem
Dirichlet duality and the nonlinear Dirichlet problem
A Dirichlet problem involving critical exponents
Dirichlet Duality and the Nonlinear Dirichlet Problem on Riemanninan Manifolds
A Dirichlet problem for polyharmonic functions
🆕 Influential since 2022
Nehari manifold and fractional Dirichlet boundary value problem
BMO and Dirichlet Problem for Degenerate Beltrami Equation
The Dirichlet problem for degenerate curvature equations
On Dirichlet Problem of Time-Fractional Advection-Diffusion Equation
BMO and Dirichlet problem for degenerate Beltrami equation
📚 Books worth reading
On Dirichlet's boundary value problemChristian G. Simader · 1954
Dirichlet and Related DistributionsKai Wang Ng · 2011- 📕Multi-dimensional asymptotically stable 4th order accurate schemes for the diffusion equationSaul S. Abarbanel · 1996
- 📕La notion de point irrégulier dans le problème de DirichletFlorin Vasilesco · 1938
An introduction to potential theoryNicolaas Du Plessis · 1970- 📕Espaces de Banach réticulés et problème de DirichletMarc Rogalski · 1968
Weakly nonlinear Dirichlet problems on long or thin domainsE. N. Dancer · 1993- 📕La notion de capacitéFlorin Vasilesco · 1937
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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