Note for Elliptic PDE

Covering:
    1. Maximum principles, boundedness estimate, global & interior & logarithmical gradient estimate of uniform elliptic equations;
    2. Basic theory of Sobolev space(definitions, inequalities, approximation, extension, trace);
    3. Weak solution of divergence type uniform elliptic equations;
    4. Bootstrap theory(Schauder theory, De Giorgi theory, Evans-Krylov estimate, Krylov-Safonov estimate);
    5. Linear evolution equations(weak solutions of parabolic equation and hyperbolic equation).
Reference: Lecture note of Ma, textbooks from Evans, Gilbarg & Trudinger, Liu Q. & Han F.H.