We know that the solution of -\Delta u=f in B_1 is x_N-odd when f is x_N odd.
I guess you assume Dirichelet bc so that the above problem is uniquely solvable in Holder spaces, since h(t)=|t|^pt is C^1 and increasing. If v(x',x_N)=-u(x',-x_N), then v solves the same problem as u, hence u=v.
Thanks, I got it.
All-purpose ofcgtrnbserver for any variety of models has been synthesized.
04 May 2017 3,683 3 View
07 August 2016 1,750 0 View
07 August 2016 8,467 2 View
11 December 2015 2,901 6 View
05 June 2015 5,361 1 View
The regional fractional laplacian is defined by (-\Delta)_D^a u(x)=-C P:V. \int_D\frac{u(y)-u(z)}{|y-z|^{N+2a}}dy, where D is a C^2 domain.
10 November 2014 1,530 5 View
Boundary blow-up solution is usually found by Perron's method in the classical sense.
02 March 2014 1,130 2 View
I have two groups of brain samples, control and treated for example. It was total RNA nova seq sequencing. I tried all the available pipeline like: star+rsem+deseq2, Hista+stringtie+cuffdiff,...
27 February 2021 356 6 View
As it is highly probable that pellets will have a higher degree of air gaps and voids than thin films, is it possible to pole the samples with corona poling nevertheless? Or is there the...
24 February 2021 1,349 1 View
I recently came across a paper focusing on the hydrodeoxygenation of oxygen-containing compounds. The paper linearized the rate equation in order to determine the experimental reaction order with...
14 February 2021 8,254 2 View
Respected Scientific Community. I'm interested to carry out experimental studies on a circular cylinder. But even after doing literature review I unable to get the exact design of the cylinder...
10 February 2021 6,221 1 View
Asking this as Google forms doesn't allow multiple items in a semantic differential format.
04 February 2021 5,869 4 View
I used Generalized Estimating Equations (geepack in R) on my regularly monitored (twice a year) plant abundance data in grid cells to evaluate their trends of density. Since these are time-series...
26 January 2021 3,833 1 View
This is my very first encounter with functional equation of this kind, and methods of series solution and differential equations are of not much help. The solution to this problem, or at least the...
25 January 2021 6,053 5 View
For a function, usually sign of second derivative (and if it is zero, even/odd index of higher order derivative whose numerical value is zero) is enough to detect whether the extreme point is...
25 January 2021 7,703 3 View
Hi, I have raw data from [HG-U133_Plus_2] Affymetrix Human Genome U133 Plus 2.0 Array that I want to process using the Expresso function for Affymetrix microarrays. My samples include tumor...
22 January 2021 1,527 3 View
Is there a polynomial Hamiltonian vector field with a finite number of periodic orbits? Please see this MO question:...
21 January 2021 1,673 4 View