Context : The formation and evolution of the cosmic web is governed by the gravitational attraction of dark matter and antigravity of dark energy ( cosmological constant ) .
In the cosmic web , galaxy superclusters or their high-density cores are the largest objects that may collapse at present or during the future evolution .

Aims : We study the dynamical state and possible future evolution of galaxy superclusters from the Sloan Great Wall ( SGW ) , the richest galaxy system in the nearby Universe .

Methods : We calculated supercluster masses using dynamical masses of galaxy groups and stellar masses of galaxies .
We employed normal mixture modelling to study the structure of rich SGW superclusters and search for components ( cores ) in superclusters .
We analysed the radial mass distribution in the high-density cores of superclusters centred approximately at rich clusters and used the spherical collapse model to study their dynamical state .

Results : The lower limit of the total mass of the SGW is approximately M = 2.5 \times~ { } 10 ^ { 16 } h ^ { -1 } M _ { \odot } .
Different mass estimators of superclusters agree well , the main uncertainties in masses of superclusters come from missing groups and clusters .
We detected three high-density cores in the richest SGW supercluster ( SCl 027 ) and two in the second richest supercluster ( SCl 019 ) .
They have masses of 1.2 - 5.9 \times~ { } 10 ^ { 15 } h ^ { -1 } M _ { \odot } and sizes of up to \approx 60 h ^ { -1 } Mpc .
The high-density cores of superclusters are very elongated , flattened perpendicularly to the line of sight .
The comparison of the radial mass distribution in the high-density cores with the predictions of spherical collapse model suggests that their central regions with radii smaller than 8 h ^ { -1 } Mpc and masses of up to M = 2 \times~ { } 10 ^ { 15 } h ^ { -1 } M _ { \odot } may be collapsing .

Conclusions : The rich SGW superclusters with their high-density cores represent dynamically evolving environments for studies of the properties of galaxies and galaxy systems .