New posts in partial-differential-equations

Nonhomogeneous wave equation

partial-differential-equations wave-equation

Weakly Harmonic Functions (Weak Solutions to Laplace's Equation $\Delta u=0$) and Logic of Test Function Techniques.

analysis partial-differential-equations harmonic-functions

Solving Poisson's equation for $\varrho(\mathbf{r}) = \sigma \cos\left(\frac{2 \pi}{L} x\right) \, \delta(y)$

ordinary-differential-equations partial-differential-equations fourier-analysis

What is the Laplace operator's representation in 3-sphere-coordinates?

differential-geometry multivariable-calculus partial-differential-equations

You can't solve Laplace's equation with boundary conditions on isolated points. But why?

reference-request partial-differential-equations harmonic-functions boundary-value-problem potential-theory

Why are second order linear PDEs classified as either elliptic, hyperbolic or parabolic?

geometry ordinary-differential-equations partial-differential-equations terminology intuition

If $u_k$ converges uniformly on $\partial \Omega$, does it converge uniformly on $\Omega$?

partial-differential-equations harmonic-functions maximum-principle

Show that exist a function $u$ continuous in $\overline{\Omega}$ [duplicate]

partial-differential-equations harmonic-functions maximum-principle

Extension of partial derivatives and the definition of $C^k(\overline{\Omega})$

real-analysis partial-differential-equations notation

Homological algebra in PDE

soft-question partial-differential-equations homological-algebra big-picture

Good sources to learn about Geometric Analysis

differential-geometry reference-request partial-differential-equations

Elliptic Regularity Theorem

functional-analysis partial-differential-equations sobolev-spaces holder-spaces

Product rule of weak derivatives

real-analysis partial-differential-equations sobolev-spaces weak-derivatives

Unbounded entropy solution to Burgers' equation

partial-differential-equations hyperbolic-equations

When can one expect a classical solution of a PDE?

functional-analysis partial-differential-equations soft-question distribution-theory

Characteristics method applied to the PDE $u_x^2 + u_y^2=u$

ordinary-differential-equations partial-differential-equations

What connections are there between number theory and partial differential equations?

number-theory partial-differential-equations

Evans pde book: details on an bound for a Sobolev norm in the proof of the Meyers-Serrin theorem

partial-differential-equations proof-verification sobolev-spaces

Dirichlet problem on $[0,1] \times [0, \pi]$

partial-differential-equations fourier-analysis

Define vector field with known curl and div [duplicate]

partial-differential-equations vector-analysis physics vector-fields laplacian