Question

Equation $\nabla(\phi) = \nabla\times \bf{A}$ on a (2D) square.

score 92 · Answer 1 · 2026-03-25 08:07:57

92

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Equation $\nabla(\phi) = \nabla\times \bf{A}$ on a (2D) square.

Published on 25 Mar 2026 - 8:07

score 117 · Answer 2 · 2018-06-10 04:23:26

117

Views

system of partial differential equations

Published on 10 Jun 2018 - 4:23

score 157 · Answer 3 · 2026-03-29 15:16:55

157

Views

How to get $[(-\Delta+\lambda)^{-1}u](x)=\int_{\mathbb{R}^3}\frac{\exp(-\sqrt{\lambda}\vert x-y \vert )}{4\pi \vert x-y \vert}u(y)dy$

Published on 29 Mar 2026 - 15:16

score 165 · Answer 4 · 2026-03-27 12:20:02

165

Views

Prove that $\lim\limits_{|x|\rightarrow \infty} u(x) = 0$ for $u \in W^{1,p}(\mathbb{R}^n).$

Published on 27 Mar 2026 - 12:20

score 78 · Answer 5 · 2026-03-25 19:10:04

Solve the PDE: $(xy-x^2)\frac{\partial u}{\partial x} + y^2 \frac{\partial u}{\partial y} + (e^{y/x}+yz)\frac{\partial u}{\partial z} = 0$

score 323 · Answer 6 · 2026-04-06 04:32:47

323

Views

Uniqueness of the Neumann problem

Published on 06 Apr 2026 - 4:32

score 595 · Answer 7 · 2026-04-04 15:57:12

595

Views

Every $L^2$ function is the divergence of a $L^2$ vector field

Published on 04 Apr 2026 - 15:57

score 120 · Answer 8 · 2026-03-25 02:12:12

120

Views

why is there a division by zero in the formula of the characteristic equations for a homogeneous first order pde ??

Published on 25 Mar 2026 - 2:12

score 25 · Answer 9 · 2018-06-11 03:29:26

Minimization of $||\nabla \phi(\cdot+x_0)e^{i\gamma} - \nabla R(\cdot)||_{L^2}^2 + E||\phi(\cdot + x_0)e^{i\gamma}-R(\cdot)||_{L^2}^2$

score 54 · Answer 10 · 2026-03-26 18:49:57

54

Views

Classifying evolution operators with always-positive outputs given positive initial conditions

Published on 26 Mar 2026 - 18:49

score 250 · Answer 11 · 2026-03-25 13:53:33

250

Views

An explicit form for a solution of a 1st order PDE

Published on 25 Mar 2026 - 13:53

score 50 · Answer 12 · 2026-03-25 06:08:28

50

Views

How to express some coefficient of a generating function using only its derivatives

Published on 25 Mar 2026 - 6:08

score 80 · Answer 13 · 2026-03-25 06:13:05

80

Views

Regularity of the "abstract" solution of the heat equation with non smooth coefficient in front of time derivative

Published on 25 Mar 2026 - 6:13

score 16 · Answer 14 · 2026-03-26 01:34:57

16

Views

Growth/boundedness of the excess of a function

Published on 26 Mar 2026 - 1:34

score 457 · Answer 15 · 2026-03-25 07:41:50

457

Views

Relation between a solution of Eikonal equation and curvature.

Published on 25 Mar 2026 - 7:41

List Question

Equation $\nabla(\phi) = \nabla\times \bf{A}$ on a (2D) square.

system of partial differential equations

How to get $[(-\Delta+\lambda)^{-1}u](x)=\int_{\mathbb{R}^3}\frac{\exp(-\sqrt{\lambda}\vert x-y \vert )}{4\pi \vert x-y \vert}u(y)dy$

Prove that $\lim\limits_{|x|\rightarrow \infty} u(x) = 0$ for $u \in W^{1,p}(\mathbb{R}^n).$

Solve the PDE: $(xy-x^2)\frac{\partial u}{\partial x} + y^2 \frac{\partial u}{\partial y} + (e^{y/x}+yz)\frac{\partial u}{\partial z} = 0$

Uniqueness of the Neumann problem

Every $L^2$ function is the divergence of a $L^2$ vector field

why is there a division by zero in the formula of the characteristic equations for a homogeneous first order pde ??

Minimization of $||\nabla \phi(\cdot+x_0)e^{i\gamma} - \nabla R(\cdot)||_{L^2}^2 + E||\phi(\cdot + x_0)e^{i\gamma}-R(\cdot)||_{L^2}^2$

Classifying evolution operators with always-positive outputs given positive initial conditions

An explicit form for a solution of a 1st order PDE

How to express some coefficient of a generating function using only its derivatives

Regularity of the "abstract" solution of the heat equation with non smooth coefficient in front of time derivative

Growth/boundedness of the excess of a function

Relation between a solution of Eikonal equation and curvature.

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