# Tagged Questions

Questions about linear partial differential equations. Often used in combination with the top-level tag ap.analysis-of-pdes.

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### Existence of solution to first order pde [closed]

Let $U : = \big(-\frac 12, \frac 12 \big)^2 \setminus B_R(0)$ for some sufficiently small $R > 0$. I would like to prove the existence of a solution $\rho = \rho (x_1, x_2)\in C^1(U)$ to the ...
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### Boundary Conditions for Linear PDEs using “Lagrange Multipliers”

Is there a way to take a linear PDE with homogeneous boundary conditions and somehow change the differential operator to include a sort of "Lagrange Multiplier" and then have a more complex (not ...
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### Regularity of a flux induced by a potential

Take $\Omega\subset R^n$ with smooth boundary (take a ball for example) a function $f\in L^{\infty}(\Omega)$ with support strictly contained in $\Omega$ and with $\int _{\Omega} f \; dx=0$ a ...
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### Regularity up to the boundary for the Poisson problem

It seems that the following assertion is widely accepted: For $k\in\mathbb N$, $p\geq 2$, $\Omega \subset \mathbb R^n$ bounded with $\partial\Omega\in C^{k+2}$ and $f\in W^{k,p}(\Omega)$, the weak ...
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