Jude Law is mobbed by theatre-goers at the stage-door of the Donmar West End theatre after critical acclaim of the first week of his run of Hamlet.

To be or not to be on Broadway.

That is the question being mulled since Michael Grandage’s Donmar West End production of “Hamlet,” starring Jude Law, opened June 3 at Wyndham’s Theater to mostly strong reviews. Rialto producers and theater owners reportedly will be traveling to London to check out the revival for a possible New York run.

Previous Donmar Warehouse productions that yielded Gotham transfers include “Cabaret,” “Frost/Nixon” and the current “Mary Stuart.” If Law does bring his Hamlet to town, it will be the first visit of Shakespeare’s brooding Danish prince to Broadway since Ralph Fiennes won a Tony for the role in 1995.

Here’s what the London critics said:

* While noting that past “Hamlet” productions have been more personal and political, Variety’s David Benedict called Law’s portrayal “riveting, thrillingly vital.” He wrote: “The outstanding quality of this assured incarnation of Shakespeare’s richest work is its unerring sense of completeness.”

* BBC News’ Caroline Briggs rated Law’s performance “fine and solid” and “one that will surely answer those who sniffed at the casting.” However, she had less praise for Kevin McNally’s Claudius and David Burke’s gravedigger.

* While he lamented Grandage’s incorporation of ambient background music and found McNally’s Claudius “pathetically bland,” the Telegraph’s Charles Spencer was a major proponent of the show: “Anyone who loves the play will enjoy this ‘Hamlet,’ but the people I envy most are those who see it for the first time in this thrilling and deeply felt production.”

* The Observer’s Susannah Clapp joined the support team for Law’s Hamlet, but gave special plaudits to one of his co-stars: “Gertrude is one of the most unrewarding of parts. … But Penelope Wilton makes observation into an activity.”

* The London Evening Standard’s Henry Hitchings declared the strength of Law’s performance “impossible to deny,” but acknowledged “other roles have been less effectively cast.”

* Michael Billington in the Guardian found the production lacking in social and political context but nonetheless judged it “a swift, clear, well-staged version of Shakespeare’s most exciting play.”

n The Times’ Christopher Hart gave the show a mixedreview, calling Law’s work “a perfectly solid and respectable performance” but “not a Hamlet that will still be talked about in 10 years’ time.”

* The Independent’s Michael Coveney wrote perhaps the most damaging review, blasting Law’s performance as a disappointment: “For a start he’s not funny, which is sad given he’s playing the wittiest tragic hero ever written. His speed of speech is a terrible affliction. And he looks like someone en route to the gym, in his grey sweatshirt and baggy pantaloons.”

Law previously appeared on Broadway in 1995 in the National Theater production of Jean Cocteau’s “Indiscretions,” scoring a Tony nom for featured actor. If he does transfer with “Hamlet,” he will join a distinguished list of actors to tackle the role on the Rialto including Sam Waterston, Richard Burton, Leslie Howard, John Gielgud, John Barrymore and Edwin Booth.

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Jude Law channels his inner Hamlet and grabs hold of costar Gugu Mbatha-Raw (as Ophelia) in this new still from the stage production of Hamlet at Wyndham’s Theater in London.

Other pictures below include Jude leaving Wyndham’s on Thursday (June 11). Hamlet is playing through Aug. 22 at Wyndham’s Theater.

The NY Times reviews Jude in the show, saying, “Fierce-eyed, charismatic, gestural to a degree one wouldn’t expect from a character who makes a point of advising the Players not to ’saw the air.’ One can imagine his particular empathy for this play given that London must at times seem for Mr. Law one large Elsinore, the tabloid press shadowing this fine actor’s every move to a degree unknown even at Denmark’s intrigue-laden Kronborg Castle.”

To see the pictures, visit the Just Jared site.

Jude Law attends the afterparty following the press night of ‘Hamlet’, at The National Cafe on June 3, 2009 in London, England.

Jude Law as “Hamlet” directed by Michael Grandage at Wyndham’s Theatre

Jude Law has received whistles and cheers at a production of Hamlet in which he plays the title role.

The play is directed by Michael Grandage and also stars Penelope Wilton as Gertrude.

Law mouthed “thank you” at the audience for their reception.

Law played the role with ruffled hair and wearing dark clothing. Cast members were dressed in modern-day costume on the sparsely lit stage which had a grey stone background.

Law played the role with a lightness of touch that raised laughter in the right places.

His “to be or not to be” speech was delivered amid a backdrop of falling snow.

Doctor Who star David Tennant recently played Hamlet in a critically acclaimed Royal Shakespeare Company production.

Law, 36, was recently quoted by the Daily Telegraph as saying: “Hamlet is a bit like a great song that’s been covered by a load of different singers.”

He said it was a part he had always wanted to play, adding: “Every job is a little daunting. This is a little more daunting than others.”

Jude Law greets fans and signs autographs after his performance in ‘Hamlet’ at the Wyndham’s Theatre in London on May 31.