I would like to make this property assertion "on the class" in such a
way that a reasoner could infer the property to be had by all of its
members, thus without needing an explicit assertion for each.
(obtaining something similar to a class-based object-oriented property
inheritance)
If you want to say that every member of some class C has individual v as the value for property p, you can write:
C subClassOf (p value v)
Now, regarding your additional comment:
I have found the same question only here, but the only answer suggests an inappropriate solution: to make the class a subclass of a
property restriction class. This leads the reasoner to infer the class
to be equivalent to the Nothing class (since there are no named
individuals with such property), thus creating an inconsistence
because of the assignment of individuals to it.
What I've just suggested is the same as what's described in that answer. There's nothing inconsistent about saying "C subClassOf (p value v)", even if there are no declared named individuals of type C. If you're running into some particular problem with this type of solution, you may want to elaborate on it (and perhaps ask an additional question); the axiom C subClassOf (p value v) subsumes the SWRL rule C(?c) → p(?c,v). (The SWRL rule is less general because it only applies to named individuals, whereas the axiom applies to all individuals.)
Example
Figure 1: C is a subclass of (p value v).

Figure 2: When a reasoner has been enabled, individual c of type C is inferred to have v as a value for property p.

Ontology (TTL and RDF/XML)
@prefix : <http://stackoverflow.com/q/29075078/1281433#> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix owl: <http://www.w3.org/2002/07/owl#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
:c a owl:NamedIndividual , :C .
:C a owl:Class ;
rdfs:subClassOf [ a owl:Restriction ;
owl:hasValue :v ;
owl:onProperty :p
] .
:p a owl:ObjectProperty .
: a owl:Ontology .
:v a owl:Thing , owl:NamedIndividual .
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:owl="http://www.w3.org/2002/07/owl#"
xmlns:xsd="http://www.w3.org/2001/XMLSchema#"
xmlns="http://stackoverflow.com/q/29075078/1281433#"
xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#">
<owl:Ontology rdf:about="http://stackoverflow.com/q/29075078/1281433#"/>
<owl:Class rdf:about="http://stackoverflow.com/q/29075078/1281433#C">
<rdfs:subClassOf>
<owl:Restriction>
<owl:onProperty>
<owl:ObjectProperty rdf:about="http://stackoverflow.com/q/29075078/1281433#p"/>
</owl:onProperty>
<owl:hasValue>
<owl:Thing rdf:about="http://stackoverflow.com/q/29075078/1281433#v">
<rdf:type rdf:resource="http://www.w3.org/2002/07/owl#NamedIndividual"/>
</owl:Thing>
</owl:hasValue>
</owl:Restriction>
</rdfs:subClassOf>
</owl:Class>
<owl:NamedIndividual rdf:about="http://stackoverflow.com/q/29075078/1281433#c">
<rdf:type rdf:resource="http://stackoverflow.com/q/29075078/1281433#C"/>
</owl:NamedIndividual>
</rdf:RDF>