User Luis Yanka Annalisc

7 votes

2 answers

2k views

Why don't we study hyperbolic equations as elliptic and parabolic equations?

asked May 6 at 1:31

5 votes

2 answers

379 views

How to prove the second Korn inequality?

fa.functional-analysis real-analysis elliptic-pde

asked Sep 4, 2021 at 3:36

4 votes

2 answers

642 views

Taylor expansion of the square of the distance function on a Riemannian manifold [closed]

riemannian-geometry curvature

asked May 25, 2021 at 16:05

4 votes

2 answers

182 views

How to prove $ \sum_{k=1}^{n}f(a_k)\leq nf\left(\frac{b}{n}\right) $ for sufficiently large $ n $ here?

ca.classical-analysis-and-odes convexity

asked Mar 13 at 12:12

4 votes

1 answer

220 views

Does the homeomorphism have a non-negative or non-positive determinant?

real-analysis ca.classical-analysis-and-odes differential-calculus

asked Apr 15 at 11:04

3 votes

0 answers

96 views

$ f,g\in \mathrm{VMO} $ but $ f\cdot g\notin \mathrm{VMO} $

fa.functional-analysis banach-spaces banach-algebras

asked Mar 7 at 13:43

3 votes

0 answers

101 views

How can I show that the map of cut point is continuous?

dg.differential-geometry riemannian-geometry

asked Jun 21, 2021 at 16:23

3 votes

0 answers

92 views

A question of the book "Regularity Theory for elliptic PDE"

elliptic-pde regularity

asked Oct 8, 2021 at 8:27

2 votes

0 answers

86 views

Some problems about energy estimates of elliptic equation

ap.analysis-of-pdes elliptic-pde

asked Nov 26, 2021 at 12:08

2 votes

0 answers

46 views

The Green function for elliptic systems in two dimensions

elliptic-pde green-function

asked Dec 15, 2021 at 15:57

2 votes

0 answers

217 views

Caccioppoli inequality in $ \mathbb{R}^2 $

ap.analysis-of-pdes elliptic-pde

asked Dec 17, 2021 at 8:28

2 votes

0 answers

59 views

How to learn Strichartz estimates for wave equations?

ap.analysis-of-pdes hyperbolic-pde wave-equation

asked Feb 12 at 11:42

2 votes

1 answer

146 views

The behavior of $ \nabla u $ on the boundary for Poisson equations

ap.analysis-of-pdes elliptic-pde

asked Mar 3 at 14:18

1 vote

1 answer

78 views

Wave equation in $ \Omega\times(0,T) $

ap.analysis-of-pdes hyperbolic-pde wave-equation

asked Apr 19 at 16:13

1 vote

0 answers

114 views

How to deal with the boundary estimate for the Schauder estimates of laplacian equations?

ap.analysis-of-pdes elliptic-pde

asked Oct 3, 2021 at 3:03

1 vote

1 answer

135 views

How to prove Poincaré inequality by using extension theorem?

real-analysis ca.classical-analysis-and-odes sobolev-spaces

asked Oct 5, 2021 at 6:56

1 vote

0 answers

50 views

What is the the "method of ascending" in the study of elliptic systems in dimension two?

ap.analysis-of-pdes elliptic-pde

asked Jan 1 at 9:05

1 vote

0 answers

54 views

Boundary estimates for elliptic systems

real-analysis ap.analysis-of-pdes elliptic-pde

asked Jan 4 at 12:17

1 vote

0 answers

61 views

Elliptic systems with two dimensions

real-analysis ap.analysis-of-pdes elliptic-pde

asked Jan 7 at 13:16

1 vote

1 answer

127 views

How to prove the reverse Hölder inequality for Laplace equations?

fa.functional-analysis real-analysis ap.analysis-of-pdes

asked Sep 12, 2021 at 12:32

1 vote

1 answer

122 views

Is the Poisson formula valid when the boundary condition is $ L^2 $?

real-analysis ap.analysis-of-pdes elliptic-pde

asked Sep 17, 2021 at 16:08

0 votes

0 answers

68 views

How to prove the regular result of elliptic equation $ -\operatorname{div}(A(x)\triangledown u)=F $ in $ B(0,1) $ if $ A $ has the Holder regularity?

ap.analysis-of-pdes elliptic-pde

asked Sep 19, 2021 at 8:00

0 votes

0 answers

67 views

Is Poisson formula valid for the weak solution of Laplacian?

ap.analysis-of-pdes elliptic-pde

asked Sep 19, 2021 at 10:59

0 votes

1 answer

127 views

Why the symmetry for all directions implies the radial symmetry?

ca.classical-analysis-and-odes

asked Aug 13, 2021 at 12:40

0 votes

0 answers

60 views

How can I show $ H^{1/2}(\partial\Omega;\mathbb{R}^m)\subset \operatorname{Trace}\left(H^{1}(\Omega;\mathbb{R}^m)\right) $ is true?

sobolev-spaces calculus-of-variations

asked Aug 18, 2021 at 7:47

0 votes

0 answers

56 views

Why the distribution of M(t) is the same as X(t)?

stochastic-processes brownian-motion

asked May 27, 2021 at 2:20

0 votes

1 answer

210 views

$f'(x)>f(f(x))$ implies $f(f(f(x)))\leq0$ for nonnegative $x$

real-analysis differential-calculus

asked Feb 28 at 13:25

0 votes

0 answers

74 views

The spectrum of Laplacian operator

fa.functional-analysis ap.analysis-of-pdes elliptic-pde eigenvalues

asked Apr 24 at 9:42

0 votes

0 answers

38 views

Resolvent and evolution equations

fa.functional-analysis ap.analysis-of-pdes parabolic-pde hyperbolic-pde

asked May 22 at 13:26

-1 votes

1 answer

61 views

Applications and motivations of resolvent for elliptic operator

fa.functional-analysis ap.analysis-of-pdes elliptic-pde sp.spectral-theory

asked May 16 at 11:38

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30 Questions

Why don't we study hyperbolic equations as elliptic and parabolic equations?

How to prove the second Korn inequality?

Taylor expansion of the square of the distance function on a Riemannian manifold [closed]

How to prove $ \sum_{k=1}^{n}f(a_k)\leq nf\left(\frac{b}{n}\right) $ for sufficiently large $ n $ here?

Does the homeomorphism have a non-negative or non-positive determinant?

$ f,g\in \mathrm{VMO} $ but $ f\cdot g\notin \mathrm{VMO} $

How can I show that the map of cut point is continuous?

A question of the book "Regularity Theory for elliptic PDE"

Some problems about energy estimates of elliptic equation

The Green function for elliptic systems in two dimensions

Caccioppoli inequality in $ \mathbb{R}^2 $

How to learn Strichartz estimates for wave equations?

The behavior of $ \nabla u $ on the boundary for Poisson equations

Wave equation in $ \Omega\times(0,T) $

How to deal with the boundary estimate for the Schauder estimates of laplacian equations?

How to prove Poincaré inequality by using extension theorem?

What is the the "method of ascending" in the study of elliptic systems in dimension two?

Boundary estimates for elliptic systems

Elliptic systems with two dimensions

How to prove the reverse Hölder inequality for Laplace equations?

Is the Poisson formula valid when the boundary condition is $ L^2 $?

How to prove the regular result of elliptic equation $ -\operatorname{div}(A(x)\triangledown u)=F $ in $ B(0,1) $ if $ A $ has the Holder regularity?

Is Poisson formula valid for the weak solution of Laplacian?

Why the symmetry for all directions implies the radial symmetry?

How can I show $ H^{1/2}(\partial\Omega;\mathbb{R}^m)\subset \operatorname{Trace}\left(H^{1}(\Omega;\mathbb{R}^m)\right) $ is true?

Why the distribution of M(t) is the same as X(t)?

$f'(x)>f(f(x))$ implies $f(f(f(x)))\leq0$ for nonnegative $x$

The spectrum of Laplacian operator

Resolvent and evolution equations

Applications and motivations of resolvent for elliptic operator