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Exercise 6 Let n (0,1). Assume that a,b,c € C1(2) such that a > @0 > 0, c _6'/2 20. Show that for any f,g € L?(0) there exists a unique u â...

Question

Exercise 6 Let n (0,1). Assume that a,b,c € C1(2) such that a > @0 > 0, c _6'/2 20. Show that for any f,g € L?(0) there exists a unique u € H} (0) such that au' v' + bu'v + cuv dc = J fv+gv dc, e H8 ($2) ,and estimate the Fl_norm of u in terms of and g.

Exercise 6 Let n (0,1). Assume that a,b,c € C1(2) such that a > @0 > 0, c _6'/2 20. Show that for any f,g € L?(0) there exists a unique u € H} (0) such that au' v' + bu'v + cuv dc = J fv+gv dc, e H8 ($2) , and estimate the Fl_norm of u in terms of and g.



Answers

a. Compute proja $2 \mathbf{u}$ b. What is proju $c \mathbf{u}$ for any $c>0 ?$


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