By Professor Dr. Stuart S. Antman, Professor Dr. Haïm Brezis, Professor Dr. Bernard D. Coleman, Professor Dr. Martin Feinberg, Professor Dr. John A. Nohel, Professor Dr. William P. Ziemer (auth.)
The 39 papers during this assortment are committed often to the precise mathematical research of difficulties in continuum mechanics, but in addition to difficulties of a only mathematical nature generally attached to partial differential equations from continuum physics. the entire papers are devoted to J. Serrin and have been initially released within the "Archive of Rational Mechanics and Analysis".
Read or Download Analysis and Continuum Mechanics: A Collection of Papers Dedicated to J. Serrin on His Sixtieth Birthday PDF
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Additional resources for Analysis and Continuum Mechanics: A Collection of Papers Dedicated to J. Serrin on His Sixtieth Birthday
E. < max J(u) < max J1(u) = fl = uEr. uEYl <% <% = max J(u) , uEy. r. that is, also <% is achieved in YI E Next we assert that there is a U1 E YI such that JI(UI) = 0 and J(Ut) = <%. Suppose this is not so. IJ'(U)/I > 15 on Y. = YI (\ J-t[<% - e, <% + e]. Thus /I J'(u] /I >15/2 on some neighborhood U. of Ye. 30) 1J(0, x) =x and for all x E E, where tp is a cut-off function so chosen that tp is positive in U. and vanishes identically outside U•. Yl) < <%, a contradiction. This proves our assertion.
II Since IllMull1 = IIluolil < IIIulil for all uE CO'(R5), we extend M by continuity to have domain E; then the result 0). 15) JQ(x) IURlp+l > Rn J Q IURlp+1 BR(xR) > Min Q' 2R;;>;[x[$4R >MaxQ· BR(O) = J lulp+1 BR
0). 15) JQ(x) IURlp+l > Rn J Q IURlp+1 BR(xR) > Min Q' 2R;;>;[x[$4R >MaxQ· BR(O) = J lulp+1 BR