As you may know, Kernel 3.19 has reached EOL (end of life), but because it is used by default on Ubuntu 15.04 Vivid Vervet, the development has been adopted by Canonical.

Recently, Kernel 3.19.8 CKT17 has been released, bringing bug-fixes only.
Installation instructions:
Compiling a Linux kernel is a little difficult and takes some time, but the Ubuntu (and derivative) users do not have to worry about that, because Canonical provides deb packages for these systems, via its kernel.ubuntu.com repository.
The below commands are available for all the Ubuntu, Linux Mint, Elementary OS, Pinguy OS, Deepin and other Ubuntu derivative systems like Peppermint, LXLE, Linux Lite, Voyager etc. Pay attention to download and install the Kernel patch for your system’s architecture (i386 debs for 32 bit systems and amd64 debs for 64 bit systems).
How to install Kernel 3.19.8 on 32 bit Ubuntu and derivative systems:
Download the needed packages:
$ cd /tmp
$ wget \
kernel.ubuntu.com/~kernel-ppa/mainline/v3.19.8-ckt17-vivid/linux-headers-3.19.8-031908ckt17_3.19.8-031908ckt17.201603211131_all.deb \
kernel.ubuntu.com/~kernel-ppa/mainline/v3.19.8-ckt17-vivid/linux-headers-3.19.8-031908ckt17-generic_3.19.8-031908ckt17.201603211131_i386.deb \
kernel.ubuntu.com/~kernel-ppa/mainline/v3.19.8-ckt17-vivid/linux-image-3.19.8-031908ckt17-generic_3.19.8-031908ckt17.201603211131_i386.deb
Install the Kernel:
$ sudo dpkg -i linux-headers-3.19*.deb linux-image-3.19*.deb
Optional, remove the kernel:
$ sudo apt-get remove linux-headers-3.19* linux-image-3.19*
How to install Kernel 3.19.8 on 64 bit Ubuntu and derivative systems:
Download the needed packages:
$ cd /tmp
$ wget \
kernel.ubuntu.com/~kernel-ppa/mainline/v3.19.8-ckt17-vivid/linux-headers-3.19.8-031908ckt17_3.19.8-031908ckt17.201603211131_all.deb \
kernel.ubuntu.com/~kernel-ppa/mainline/v3.19.8-ckt17-vivid/linux-headers-3.19.8-031908ckt17-generic_3.19.8-031908ckt17.201603211131_amd64.deb \
kernel.ubuntu.com/~kernel-ppa/mainline/v3.19.8-ckt17-vivid/linux-image-3.19.8-031908ckt17-generic_3.19.8-031908ckt17.201603211131_amd64.deb
Install the Kernel:
$ sudo dpkg -i linux-headers-3.19*.deb linux-image-3.19*.deb
Optional, remove the kernel:
$ sudo apt-get remove linux-headers-3.19* linux-image-3.19*