id sid tid token lemma pos dv13zs28169 1 1 it it PRON dv13zs28169 1 2 is be AUX dv13zs28169 1 3 shown show VERB dv13zs28169 1 4 that that SCONJ dv13zs28169 1 5 the the DET dv13zs28169 1 6 data data NOUN dv13zs28169 1 7 - - PUNCT dv13zs28169 1 8 to to ADP dv13zs28169 1 9 - - PUNCT dv13zs28169 1 10 solution solution NOUN dv13zs28169 1 11 map map NOUN dv13zs28169 1 12 for for ADP dv13zs28169 1 13 the the DET dv13zs28169 1 14 hyperelastic hyperelastic ADJ dv13zs28169 1 15 rod rod NOUN dv13zs28169 1 16 equation equation NOUN dv13zs28169 1 17 is be AUX dv13zs28169 1 18 not not PART dv13zs28169 1 19 uniformly uniformly ADV dv13zs28169 1 20 continuous continuous ADJ dv13zs28169 1 21 on on ADP dv13zs28169 1 22 bounded bound VERB dv13zs28169 1 23 sets set NOUN dv13zs28169 1 24 of of ADP dv13zs28169 1 25 sobolev sobolev NOUN dv13zs28169 1 26 spaces space NOUN dv13zs28169 1 27 with with ADP dv13zs28169 1 28 exponent exponent NOUN dv13zs28169 1 29 greater great ADJ dv13zs28169 1 30 than than ADP dv13zs28169 1 31 3/2 3/2 NUM dv13zs28169 1 32 in in ADP dv13zs28169 1 33 the the DET dv13zs28169 1 34 periodic periodic ADJ dv13zs28169 1 35 case case NOUN dv13zs28169 1 36 and and CCONJ dv13zs28169 1 37 non non ADJ dv13zs28169 1 38 - - ADJ dv13zs28169 1 39 periodic periodic ADJ dv13zs28169 1 40 cases case NOUN dv13zs28169 1 41 . . PUNCT dv13zs28169 2 1 the the DET dv13zs28169 2 2 proof proof NOUN dv13zs28169 2 3 is be AUX dv13zs28169 2 4 based base VERB dv13zs28169 2 5 on on ADP dv13zs28169 2 6 the the DET dv13zs28169 2 7 method method NOUN dv13zs28169 2 8 of of ADP dv13zs28169 2 9 approximate approximate ADJ dv13zs28169 2 10 solutions solution NOUN dv13zs28169 2 11 and and CCONJ dv13zs28169 2 12 well well ADV dv13zs28169 2 13 - - PUNCT dv13zs28169 2 14 posedness posedness NOUN dv13zs28169 2 15 estimates estimate NOUN dv13zs28169 2 16 for for ADP dv13zs28169 2 17 the the DET dv13zs28169 2 18 solution solution NOUN dv13zs28169 2 19 and and CCONJ dv13zs28169 2 20 its its PRON dv13zs28169 2 21 lifespan lifespan NOUN dv13zs28169 2 22 . . PUNCT dv13zs28169 3 1 building build VERB dv13zs28169 3 2 upon upon SCONJ dv13zs28169 3 3 this this DET dv13zs28169 3 4 work work NOUN dv13zs28169 3 5 , , PUNCT dv13zs28169 3 6 we we PRON dv13zs28169 3 7 also also ADV dv13zs28169 3 8 prove prove VERB dv13zs28169 3 9 that that SCONJ dv13zs28169 3 10 the the DET dv13zs28169 3 11 data data NOUN dv13zs28169 3 12 - - PUNCT dv13zs28169 3 13 to to ADP dv13zs28169 3 14 - - PUNCT dv13zs28169 3 15 solution solution NOUN dv13zs28169 3 16 map map NOUN dv13zs28169 3 17 for for ADP dv13zs28169 3 18 the the DET dv13zs28169 3 19 hyperelastic hyperelastic ADJ dv13zs28169 3 20 rod rod NOUN dv13zs28169 3 21 equation equation NOUN dv13zs28169 3 22 is be AUX dv13zs28169 3 23 h'older h'older ADJ dv13zs28169 3 24 continuous continuous ADJ dv13zs28169 3 25 from from ADP dv13zs28169 3 26 bounded bound VERB dv13zs28169 3 27 sets set NOUN dv13zs28169 3 28 of of ADP dv13zs28169 3 29 sobolev sobolev NOUN dv13zs28169 3 30 spaces space NOUN dv13zs28169 3 31 with with ADP dv13zs28169 3 32 exponent exponent PROPN dv13zs28169 3 33 s s X dv13zs28169 3 34 > > X dv13zs28169 3 35 3/2 3/2 NUM dv13zs28169 3 36 measured measure VERB dv13zs28169 3 37 in in ADP dv13zs28169 3 38 a a DET dv13zs28169 3 39 weaker weak ADJ dv13zs28169 3 40 sobolev sobolev NOUN dv13zs28169 3 41 norm norm NOUN dv13zs28169 3 42 with with ADP dv13zs28169 3 43 exponent exponent PROPN dv13zs28169 3 44 r r PROPN dv13zs28169 3 45 < < X dv13zs28169 3 46 s s VERB dv13zs28169 3 47 in in ADP dv13zs28169 3 48 both both DET dv13zs28169 3 49 the the DET dv13zs28169 3 50 periodic periodic ADJ dv13zs28169 3 51 and and CCONJ dv13zs28169 3 52 non non ADJ dv13zs28169 3 53 - - ADJ dv13zs28169 3 54 periodic periodic ADJ dv13zs28169 3 55 cases case NOUN dv13zs28169 3 56 . . PUNCT dv13zs28169 4 1 the the DET dv13zs28169 4 2 proof proof NOUN dv13zs28169 4 3 is be AUX dv13zs28169 4 4 based base VERB dv13zs28169 4 5 on on ADP dv13zs28169 4 6 energy energy NOUN dv13zs28169 4 7 estimates estimate NOUN dv13zs28169 4 8 coupled couple VERB dv13zs28169 4 9 with with ADP dv13zs28169 4 10 a a DET dv13zs28169 4 11 delicate delicate ADJ dv13zs28169 4 12 commutator commutator NOUN dv13zs28169 4 13 estimate estimate NOUN dv13zs28169 4 14 and and CCONJ dv13zs28169 4 15 multiplier multipli ADJ dv13zs28169 4 16 estimate estimate NOUN dv13zs28169 4 17 . . PUNCT