Question

Is the eigenfunction corresponding to the principal eigenvalue positive within $U$ when $a^{ij} \in L^\infty(U)$?

score 642 · Answer 1 · 2026-03-25 23:56:43

642

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Is the eigenfunction corresponding to the principal eigenvalue positive within $U$ when $a^{ij} \in L^\infty(U)$?

Published on 25 Mar 2026 - 23:56

score 304 · Answer 2 · 2021-05-12 23:08:27

304

Views

$f$ analytic in neighborhood of closure of $\mathbb{D}$. If $f$ is real on boundary of $\mathbb{D}$ then $f$ is constant.

Published on 12 May 2021 - 23:08

score 97 · Answer 3 · 2021-06-01 13:28:08

97

Views

Limit commutes with $\min$.

Published on 01 Jun 2021 - 13:28

score 21 · Answer 4 · 2026-03-25 18:52:27

21

Views

Is this solution in stochastic optimal control problem equivalent?

Published on 25 Mar 2026 - 18:52

score 53 · Answer 5 · 2021-06-04 18:12:19

53

Views

Holomorphic functions $f,g$ s.t. $f = \lambda g$ with $|\lambda| = 1$

Published on 04 Jun 2021 - 18:12

score 163 · Answer 6 · 2021-06-13 14:21:04

163

Views

Maximum modulus principle for harmonic functions using complex analysis

Published on 13 Jun 2021 - 14:21

score 75 · Answer 7 · 2021-06-21 03:17:10

75

Views

How to flesh out a sketch of a proof of a corollary of the Maximum Principle?

Published on 21 Jun 2021 - 3:17

score 55 · Answer 8 · 2021-07-02 15:58:44

55

Views

$\int^b_a \dot x^2(t) dt\geq \frac{\pi ^2}{4(b-a)^2}\int^b_a x^2(t)dt$

Published on 02 Jul 2021 - 15:58

score 421 · Answer 9 · 2021-07-04 10:56:23

421

Views

Evans proof of the maximum principle for subharmonic functions

Published on 04 Jul 2021 - 10:56

score 145 · Answer 10 · 2021-07-13 14:39:12

145

Views

Laplace equation with Dirichlect boundary condition for the punctured ball

Published on 13 Jul 2021 - 14:39

score 155 · Answer 11 · 2021-07-27 20:00:40

155

Views

Is this a consequence of the maximum principle for superharmonic functions?

Published on 27 Jul 2021 - 20:00

score 213 · Answer 12 · 2021-07-30 16:33:47

213

Views

Let $f$ be analytic and Im$f(z)>0$. Show $|\frac{f(z)-f(z_0)}{f(z)-\overline{f(z_0)}}|\leq|\frac{z-z_0}{z-\overline{z_0}}|$.

Published on 30 Jul 2021 - 16:33

score 140 · Answer 13 · 2021-07-31 22:50:26

140

Views

When can we guarantee the existence of an entire function with specified values at the integers?

Published on 31 Jul 2021 - 22:50

score 142 · Answer 14 · 2021-08-03 14:12:40

142

Views

Positivity of weak solutions given positive data to elliptic pde

Published on 03 Aug 2021 - 14:12

score 121 · Answer 15 · 2021-08-07 16:46:25

121

Views

Deduce positivity of solution of linear parabolic PDE from non-negative initial data

Published on 07 Aug 2021 - 16:46

List Question

Is the eigenfunction corresponding to the principal eigenvalue positive within $U$ when $a^{ij} \in L^\infty(U)$?

$f$ analytic in neighborhood of closure of $\mathbb{D}$. If $f$ is real on boundary of $\mathbb{D}$ then $f$ is constant.

Limit commutes with $\min$.

Is this solution in stochastic optimal control problem equivalent?

Holomorphic functions $f,g$ s.t. $f = \lambda g$ with $|\lambda| = 1$

Maximum modulus principle for harmonic functions using complex analysis

How to flesh out a sketch of a proof of a corollary of the Maximum Principle?

$\int^b_a \dot x^2(t) dt\geq \frac{\pi ^2}{4(b-a)^2}\int^b_a x^2(t)dt$

Evans proof of the maximum principle for subharmonic functions

Laplace equation with Dirichlect boundary condition for the punctured ball

Is this a consequence of the maximum principle for superharmonic functions?

Let $f$ be analytic and Im$f(z)>0$. Show $|\frac{f(z)-f(z_0)}{f(z)-\overline{f(z_0)}}|\leq|\frac{z-z_0}{z-\overline{z_0}}|$.

When can we guarantee the existence of an entire function with specified values at the integers?

Positivity of weak solutions given positive data to elliptic pde

Deduce positivity of solution of linear parabolic PDE from non-negative initial data

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