變分學中的多重積分（簡體書）

The principal theme of this book is “the existence and differentiability of the solutions of variational problems involving multiple integrals.” We shall discuss the corresponding questions for single integrals only very briefly since these have been discussed adequately in every other book on the calculus of variations.Moreover， applications to engineering，physics，etc.，are not discussed at all；however，we do discuss mathematical applications to such subjects as the theory of harmonic integrals and the so-called “d-Neumann” problem （see Chapters 7 and 8）.Since the plan of the book is described in Section 1.2 below we shall merely make a few observations here.本書包含了大量科研人員學習多重積分變分問題和雙曲偏微分方程問題的材料。書中不僅是作者科研成果的總結，更是同時代該領域或者相關領域的專業人士的巨大貢獻。本書無疑會成為該領域科研人員的標準差參考書。本書的主要讀者是對數學分析有一定基礎的人員，分析專業的學生將會受益匪淺。目次：導引；半經典結果；空間H pm和H p0m；弱解的可微性；一般雙曲系統解和邊界值問題的常規定理；調和積分理論的變分法；強偽-凸流形的δ-紐曼問題；參數積分導論：兩維問題；高維Plateau問題。讀者對象：數學專業的高年級本科生、研究生和更高層次的科研人員。